{"id":1077,"date":"2026-01-14T20:07:38","date_gmt":"2026-01-14T10:07:38","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1077"},"modified":"2026-01-14T20:07:38","modified_gmt":"2026-01-14T10:07:38","slug":"year11-math-2-1-5-linear-algebra","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1077","title":{"rendered":"Year11-MATH-2-1-5 Linear algebra"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Linear algebra<\/strong> is&nbsp;&nbsp;<strong>branch of mathematics focused on vectors, matrices, and linear equations<\/strong>. In Year 11 mathematics, the subject is typically an introduction to these concepts, building upon general algebra skills.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Core Concepts Covered in Year 11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The topics introduced at this level generally form the foundations of the subject and are more computational than abstract. Key areas of study include:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Linear Equations<\/strong><strong>:<\/strong>\u00a0Solving systems of equations (e.g., simultaneous equations) with a finite number of variables. Methods often include substitution, elimination, and graphing to find the point(s) of intersection, which forms a straight line when graphed.<\/li>\n\n\n\n<li><strong>Vectors<\/strong><strong>:<\/strong>\u00a0Understanding vectors as quantities with both magnitude and direction. This involves basic operations such as vector addition and scalar multiplication.<\/li>\n\n\n\n<li><strong>Matrices<\/strong><strong>:<\/strong>\u00a0Using matrices (rectangular arrays of numbers) to organize and solve systems of linear equations more efficiently. Topics typically cover matrix operations like addition, multiplication, and finding determinants and inverses.<\/li>\n\n\n\n<li><strong>Linear Transformations<\/strong><strong>:<\/strong>\u00a0Exploring how linear functions can represent geometric transformations like rotations, reflections, and scaling in 2D or 3D space.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&gt;&gt; Linear Equations<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>In Year 11 Maths, linear equations focus on expressions where variables have a power of one (like <\/strong><math data-latex=\"x\"><semantics><mi>x<\/mi><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math><strong> or  <\/strong><math data-latex=\"y\"><semantics><mi>y<\/mi><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math><strong>, not <\/strong><math data-latex=\"x^2\"><semantics><msup><mi>x<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">x^2<\/annotation><\/semantics><\/math>), forming straight lines when graphed, and involve solving for unknown values by isolating variables using inverse operations, extending to systems of equations, inequalities, and real-world problem-solving. Key concepts include slope-intercept form (<math data-latex=\"y = mx + b\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = mx + b<\/annotation><\/semantics><\/math>), standard form (<math data-latex=\"A_x + B_y = C\"><semantics><mrow><msub><mi>A<\/mi><mi>x<\/mi><\/msub><mo>+<\/mo><msub><mi>B<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A_x + B_y = C<\/annotation><\/semantics><\/math>), solving single-variable equations with multiple steps, and applying these skills to word problems.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Core Concepts for Year 11:&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> An equation where variables are only to the power of 1 (e.g., <math data-latex=\"2x + 3 = 9\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x + 3 = 9<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li><strong>Graphical Representation<\/strong><strong>:<\/strong> Produces a straight line on a coordinate plane.<\/li>\n\n\n\n<li><strong>Forms<\/strong><strong>:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Slope-Intercept:<\/strong> <math data-latex=\"y = mx + b\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = mx + b<\/annotation><\/semantics><\/math>( <math data-latex=\"m\"><semantics><mi>m<\/mi><annotation encoding=\"application\/x-tex\">m<\/annotation><\/semantics><\/math>= slope\/gradient, <math data-latex=\"b\"><semantics><mi>b<\/mi><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>= <math data-latex=\"y\"><semantics><mi>y<\/mi><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>-intercept).<\/li>\n\n\n\n<li><strong>Standard Form:<\/strong> <math data-latex=\"Ax + By = C \"><semantics><mrow><mi>A<\/mi><mi>x<\/mi><mo>+<\/mo><mi>B<\/mi><mi>y<\/mi><mo>=<\/mo><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Ax + By = C <\/annotation><\/semantics><\/math> or <math data-latex=\"Ax + By + C = 0\"><semantics><mrow><mi>A<\/mi><mi>x<\/mi><mo>+<\/mo><mi>B<\/mi><mi>y<\/mi><mo>+<\/mo><mi>C<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">Ax + By + C = 0<\/annotation><\/semantics><\/math><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Solving Single Variable Equations:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Steps:<\/strong> Expand brackets, group like terms, simplify, and isolate the variable using inverse operations (addition\/subtraction, multiplication\/division) on both sides to maintain balance.<\/li>\n\n\n\n<li><strong>Example:<\/strong> 2(x+3) = 10 \u2192 2x + 6 = 10 \u2192 2x = 4 \u2192 x = 2 .<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Solving Two Variable Equations (Graphing)<\/strong><strong>:<\/strong> Finding (x, y) pairs that satisfy the equation, often represented by finding intercepts or points on the line.<\/li>\n\n\n\n<li><strong>Linear Inequalities<\/strong><strong>:<\/strong> Using &lt;, >, \u2264, \u2265 instead of = to represent ranges on a line.<\/li>\n\n\n\n<li><strong>Applications<\/strong><strong>:<\/strong> Using linear equations to model and solve real-life scenarios like distance\/time, finance, or mixture problems (problem-solving).\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What&#8217;s New in Year 11:&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>More Complex Multi-Step Equations<\/strong><strong>:<\/strong> Equations with variables and constants on both sides, requiring more advanced grouping and simplification.<\/li>\n\n\n\n<li><strong>Introduction to Systems of Linear Equations<\/strong><strong>:<\/strong> Solving two or more linear equations simultaneously (e.g., by substitution or elimination) to find a common solution (point of intersection).<\/li>\n\n\n\n<li><strong>Vectors<\/strong><strong>:<\/strong> Linear algebra starts introducing vectors, which are related to direction and magnitude, extending the concept of linear relationships.<\/li>\n\n\n\n<li><strong>Problem-Solving Contexts<\/strong><strong>:<\/strong> Applying these algebraic skills to more complex word problems, requiring translation from words to equations.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&gt;&gt; <\/strong><strong>Vectors<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>In Year 11 Mathematics, vectors are quantities with both\u00a0magnitude (size)\u00a0and\u00a0direction, represented visually as arrows, contrasting with scalars (numbers with onlymagnitude ). Students learn to represent them using notation like column vectors (e.g., <\/strong><math data-latex=\"\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)\"><semantics><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mtable columnalign=\"center\"><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>x<\/mi><\/mtd><\/mtr><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>y<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)<\/annotation><\/semantics><\/math>  or <math data-latex=\"i\/j \"><semantics><mrow><mi>i<\/mi><mi>\/<\/mi><mi>j<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">i\/j <\/annotation><\/semantics><\/math> notation, understand vector addition\/subtraction (head-to-tail or component-wise), calculate magnitude using Pythagoras, and apply them to problems involving displacement, velocity, and force.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Concepts\u00a0<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition<\/strong>: A vector describes movement or force, combining how far (magnitude) and where (direction).<\/li>\n\n\n\n<li><strong>Representation<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Directed Line Segment<\/strong>: An arrow from a starting point (tail) to an end point (head).<\/li>\n\n\n\n<li><strong>Column Vectors<\/strong>: <strong> <\/strong><math data-latex=\"\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)\"><semantics><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mtable columnalign=\"center\"><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>x<\/mi><\/mtd><\/mtr><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>y<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)<\/annotation><\/semantics><\/math>shows horizontal (x) and vertical (y) change.<\/li>\n\n\n\n<li><strong>i, j Notation<\/strong>: <math data-latex=\"xi + yj\"><semantics><mrow><mi>x<\/mi><mi>i<\/mi><mo>+<\/mo><mi>y<\/mi><mi>j<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">xi + yj<\/annotation><\/semantics><\/math>, where <math data-latex=\"i\"><semantics><mi>i<\/mi><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math> is the horizontal unit vector and <math data-latex=\"j \"><semantics><mi>j<\/mi><annotation encoding=\"application\/x-tex\">j <\/annotation><\/semantics><\/math> is the vertical unit vector.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magnitude<\/strong>: The length of the vector, found using the Pythagorean theorem (e.g., <math data-latex=\"|\\vec{v}|=\\sqrt{x^{2}+y^{2}}\"><semantics><mrow><mi>|<\/mi><mover><mi>v<\/mi><mo stretchy=\"false\" style=\"transform:scale(0.75) translate(10%, 30%);\">\u2192<\/mo><\/mover><mi>|<\/mi><mo>=<\/mo><msqrt><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>y<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">|\\vec{v}|=\\sqrt{x^{2}+y^{2}}<\/annotation><\/semantics><\/math> ).<\/li>\n\n\n\n<li><strong>Vector Operations<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Addition<\/strong>: Geometrically (head-to-tail), or by adding corresponding components.<\/li>\n\n\n\n<li><strong>Subtraction<\/strong>: Similar to addition, or by adding the negative (reversed) vector.<\/li>\n\n\n\n<li><strong>Scalar Multiplication<\/strong>: Multiplying a vector by a number changes its magnitude (stretches or shrinks it).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Types of Vectors<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Position Vectors<\/strong>: Start at the origin (0,0).<\/li>\n\n\n\n<li><strong>Displacement Vectors<\/strong>: Can be anywhere on the plane.<\/li>\n\n\n\n<li><strong>Unit Vectors<\/strong>: Have a magnitude of 1.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Applications<\/strong>: Explaining real-world scenarios like a plane&#8217;s ground velocity affected by wind, or forces acting on an object.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">In essence, Year 11 vectors build a bridge from basic algebra to more advanced mathematics by formalizing the concept of movement and direction, essential for physics and higher-level maths like calculus and linear algebra.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&gt;&gt; <\/strong><strong>Matrices<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In Year 11 mathematics, matrices are rectangular arrays of numbers or symbols organized into rows and columns, used to represent data and solve problems in science, economics, and computer science\u00a0, with key concepts including matrix order (dimensions like 2&#215;3), elements (entries), and basic operations like addition, subtraction (element-wise), and multiplication, often modeling real-world scenarios like sales or networks.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Concepts<\/strong>:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> A matrix is a grid of numbers, symbols, or expressions arranged in rows (horizontal) and columns (vertical).<\/li>\n\n\n\n<li><strong>Notation:<\/strong> Matrices are usually denoted by capital letters (e.g., A, B), and their entries by lowercase letters with subscripts (e.g., <math data-latex=\"a_{ij}\"><semantics><msub><mi>a<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">a_{ij}<\/annotation><\/semantics><\/math> for the element in the <math data-latex=\"i^{th}\"><semantics><msup><mi>i<\/mi><mrow><mi>t<\/mi><mi>h<\/mi><\/mrow><\/msup><annotation encoding=\"application\/x-tex\">i^{th}<\/annotation><\/semantics><\/math> row and <math data-latex=\"j^{th}\"><semantics><msup><mi>j<\/mi><mrow><mi>t<\/mi><mi>h<\/mi><\/mrow><\/msup><annotation encoding=\"application\/x-tex\">j^{th}<\/annotation><\/semantics><\/math> column).<\/li>\n\n\n\n<li><strong>Order (Dimensions):<\/strong> The size of a matrix is given as rows \u00d7 columns (e.g., a 2&#215;3 matrix has 2 rows and 3 columns).<\/li>\n\n\n\n<li><strong>Elements:<\/strong> The individual numbers or items within the matrix.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Basic Operations:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Addition\/Subtraction:<\/strong> Performed element-by-element; matrices must have the same order.<\/li>\n\n\n\n<li><strong>Scalar Multiplication:<\/strong> Multiplying a matrix by a single number (scalar), where each element is multiplied by that number.<\/li>\n\n\n\n<li><strong>Matrix Multiplication:<\/strong> A more complex operation, where the order matters (AB is usually not equal to BA) and is crucial for many applications.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Applications (Year 11 Level):&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Modeling Real-World Data:<\/strong> Representing sales figures, ticket sales, or inventory.<\/li>\n\n\n\n<li><strong>Network Diagrams:<\/strong> Describing road or communication networks (e.g., one-step or two-step connections).<\/li>\n\n\n\n<li><strong>Problem Solving:<\/strong> Solving systems of equations and analyzing data efficiently.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">In essence, matrices provide a structured way to organize and manipulate data, making them powerful tools for solving complex problems in various fields, which is a key focus in Year 11 mathematics.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&gt;&gt; <\/strong><strong>Linear Transformations<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In mathematics, linear transformations are.\u00a0typically an advanced topic studied at the university level (or equivalent advanced high school courses like AP Calculus\/Linear Algebra), rather than in standard Year 11 curriculum. The Year 11 curriculum usually focuses on foundational algebra and geometry, including basic transformations of functions like translations, reflections, and scaling.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What a Linear Transformation Is (and what it isn&#8217;t in Year 11)&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A <strong>linear transformation<\/strong> (also known as a linear map or operator) is a special kind of function between vector spaces that &#8220;preserves&#8221; the operations of vector addition and scalar multiplication.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formally, a transformation <math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math> is linear if, for any vectors <math data-latex=\"u\"><semantics><mi>u<\/mi><annotation encoding=\"application\/x-tex\">u<\/annotation><\/semantics><\/math> and <math data-latex=\"v\"><semantics><mi>v<\/mi><annotation encoding=\"application\/x-tex\">v<\/annotation><\/semantics><\/math> and any scalar <math data-latex=\"c\"><semantics><mi>c<\/mi><annotation encoding=\"application\/x-tex\">c<\/annotation><\/semantics><\/math> , it satisfies two properties:\u00a0<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Additivity<\/strong>: <math data-latex=\"T(\\mathbf{u}+\\mathbf{v})=T(\\mathbf{u})+T(\\mathbf{v})\"><semantics><mrow><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo>+<\/mo><mi>\ud835\udc2f<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2f<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">T(\\mathbf{u}+\\mathbf{v})=T(\\mathbf{u})+T(\\mathbf{v})<\/annotation><\/semantics><\/math><\/li>\n\n\n\n<li><strong>Homogeneity<\/strong>: \u00a0<math data-latex=\"T(c\\mathbf{u})=cT(\\mathbf{u})\"><semantics><mrow><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>c<\/mi><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>c<\/mi><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">T(c\\mathbf{u})=cT(\\mathbf{u})<\/annotation><\/semantics><\/math><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">These properties ensure that all straight lines remain straight lines after the transformation and that the origin stays fixed.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key Characteristics&nbsp;<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Matrices<\/strong>: Every linear transformation can be represented by a matrix multiplication. For example, geometric operations like rotations, reflections, and scaling that keep the origin fixed are linear transformations.<\/li>\n\n\n\n<li><strong>Geometric Interpretation<\/strong>: Visually, a linear transformation stretches, rotates, or shears a grid while keeping grid lines parallel and evenly spaced.<\/li>\n\n\n\n<li><strong>Origin Must Be Fixed<\/strong>: A quick check to see if a transformation is <em>not<\/em> linear is to see if it moves the origin (0,0). If a transformation moves the origin (a translation or shift), it is not a linear transformation in the mathematical sense.\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Relevance to Year 11&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the standard Australian or UK Year 11 curriculum, you are more likely to encounter <em>transformations of functions<\/em>, such as:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Translations<\/strong>: Shifting a graph up, down, left, or right (e.g., <math data-latex=\"f(x)+k\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f(x)+k<\/annotation><\/semantics><\/math> or  <math data-latex=\"f(x-h)\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mi>h<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(x-h)<\/annotation><\/semantics><\/math>).<\/li>\n\n\n\n<li><strong>Reflections<\/strong>: Flipping a graph across an axis (e.g., <math data-latex=\"-f(x)\"><semantics><mrow><mo>\u2212<\/mo><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">-f(x)<\/annotation><\/semantics><\/math> or <math data-latex=\"f(-x)\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(-x)<\/annotation><\/semantics><\/math> ).<\/li>\n\n\n\n<li><strong>Scaling<\/strong>: Stretching or compressing a graph vertically or horizontally (e.g., <math data-latex=\"af(x)\"><semantics><mrow><mi>a<\/mi><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">af(x)<\/annotation><\/semantics><\/math>).\u00a0<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">While the term &#8220;linear function&#8221; in high school usually refers to functions of the form  <math data-latex=\"f(x)=mx+b\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f(x)=mx+b<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a straight line), these are only considered a formal <em>linear transformation<\/em> if the y-intercept is zero (i.e., the line passes through the origin).\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">********************************************************************************************************************************************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7dda\u578b\u4ee3\u6570\u306f\u3001\u30d9\u30af\u30c8\u30eb\u3001\u884c\u5217\u3001\u7dda\u5f62\u65b9\u7a0b\u5f0f\u306b\u7126\u70b9\u3092\u5f53\u3066\u305f\u6570\u5b66\u306e\u4e00\u5206\u91ce\u3067\u3059<\/strong>\u300211\u5e74\u751f\u306e\u6570\u5b66\u3067\u306f\u3001\u4e00\u822c\u7684\u306b\u3053\u308c\u3089\u306e\u6982\u5ff5\u306e\u5165\u9580\u3068\u3057\u3066\u6271\u308f\u308c\u3001\u4e00\u822c\u7684\u306a\u4ee3\u6570\u306e\u30b9\u30ad\u30eb\u3092\u57fa\u76e4\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>11<\/strong><strong>\u5e74\u751f\u3067\u6271\u308f\u308c\u308b\u4e3b\u8981\u6982\u5ff5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30ec\u30d9\u30eb\u3067\u5c0e\u5165\u3055\u308c\u308b\u30c8\u30d4\u30c3\u30af\u306f\u3001\u4e00\u822c\u7684\u306b\u3053\u306e\u79d1\u76ee\u306e\u57fa\u790e\u3092\u5f62\u6210\u3059\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u62bd\u8c61\u7684\u3068\u3044\u3046\u3088\u308a\u306f\u8a08\u7b97\u7684\u306a\u5185\u5bb9\u3067\u3059\u3002\u4e3b\u306a\u5b66\u7fd2\u5206\u91ce\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7dda\u578b\u65b9\u7a0b\u5f0f<\/strong>\uff1a\u6709\u9650\u500b\u306e\u5909\u6570\u3092\u6301\u3064\u9023\u7acb\u65b9\u7a0b\u5f0f\uff08\u4f8b\uff1a\u9023\u7acb\u65b9\u7a0b\u5f0f\uff09\u3092\u89e3\u304f\u3002\u89e3\u6cd5\u306b\u306f\u3001\u4ee3\u5165\u3001\u6d88\u53bb\u6cd5\u3001\u30b0\u30e9\u30d5\u5316\u306b\u3088\u308b\u4ea4\u70b9\uff08\u30b0\u30e9\u30d5\u306b\u63cf\u304f\u3068\u76f4\u7dda\u306b\u306a\u308b\u70b9\uff09\u306e\u63a2\u7d22\u306a\u3069\u304c\u542b\u307e\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30d9\u30af\u30c8\u30eb<\/strong>\uff1a\u30d9\u30af\u30c8\u30eb\u3092\u5927\u304d\u3055\u3068\u65b9\u5411\u306e\u4e21\u65b9\u3092\u6301\u3064\u91cf\u3068\u3057\u3066\u7406\u89e3\u3059\u308b\u3002\u3053\u308c\u306b\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97\u3084\u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\u3068\u3044\u3063\u305f\u57fa\u672c\u7684\u306a\u6f14\u7b97\u304c\u542b\u307e\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u884c\u5217<\/strong>\uff1a\u884c\u5217\uff08\u6570\u5024\u306e\u9577\u65b9\u5f62\u914d\u5217\uff09\u3092\u7528\u3044\u3066\u3001\u9023\u7acb\u7dda\u5f62\u65b9\u7a0b\u5f0f\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u6574\u7406\u3057\u3001\u89e3\u304f\u3002\u30c8\u30d4\u30c3\u30af\u3067\u306f\u901a\u5e38\u3001\u52a0\u7b97\u3001\u4e57\u7b97\u3001\u884c\u5217\u5f0f\u3084\u9006\u884c\u5217\u306e\u7b97\u51fa\u3068\u3044\u3063\u305f\u884c\u5217\u6f14\u7b97\u304c\u6271\u308f\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7dda\u5f62\u5909\u63db<\/strong>\uff1a\u7dda\u5f62\u95a2\u6570\u304c2\u6b21\u5143\u307e\u305f\u306f3\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u56de\u8ee2\u3001\u53cd\u5c04\u3001\u62e1\u5927\u7e2e\u5c0f\u306a\u3069\u306e\u5e7e\u4f55\u5b66\u7684\u5909\u63db\u3092\u3069\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u308b\u304b\u3092\u63a2\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e00\u6b21\u65b9\u7a0b\u5f0f<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">11\u5e74\u751f\u306e\u6570\u5b66\u3067\u306f\u3001\u4e00\u6b21\u65b9\u7a0b\u5f0f\u306f\u5909\u6570\u304c1\u306e\u3079\u304d\u4e57\u3092\u6301\u3064\u5f0f\uff08 <math><semantics><mi>x<\/mi><\/semantics><\/math>\u3084 y\u306a\u3069\u3001<math data-latex=\"x^2\"><semantics><msup><mi>x<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">x^2<\/annotation><\/semantics><\/math> \u3067\u306f\u306a\u3044\uff09\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u76f4\u7dda\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u9006\u6f14\u7b97\u3092\u7528\u3044\u3066\u5909\u6570\u3092\u5206\u96e2\u3059\u308b\u3053\u3068\u3067\u672a\u77e5\u6570\u3092\u89e3\u304d\u3001\u9023\u7acb\u65b9\u7a0b\u5f0f\u3001\u4e0d\u7b49\u5f0f\u3001\u305d\u3057\u3066\u73fe\u5b9f\u4e16\u754c\u306e\u554f\u984c\u89e3\u6c7a\u306b\u3082\u5fdc\u7528\u3055\u308c\u307e\u3059\u3002\u4e3b\u8981\u306a\u6982\u5ff5\u306b\u306f\u3001\u50be\u304d\u30fb\u5207\u7247\u5f62\u5f0f\uff08<math data-latex=\"y = mx + b\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = mx + b<\/annotation><\/semantics><\/math>\uff09\u3001\u6a19\u6e96\u5f62\uff08<math data-latex=\"A_x = B_y = C\"><semantics><mrow><msub><mi>A<\/mi><mi>x<\/mi><\/msub><mo>=<\/mo><msub><mi>B<\/mi><mi>y<\/mi><\/msub><mo>=<\/mo><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A_x = B_y = C<\/annotation><\/semantics><\/math>\uff09\u3001\u8907\u6570\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u89e3\u304f\u4e00\u5909\u6570\u65b9\u7a0b\u5f0f\u3001\u305d\u3057\u3066\u3053\u308c\u3089\u306e\u30b9\u30ad\u30eb\u3092\u6587\u7ae0\u984c\u306b\u5fdc\u7528\u3059\u308b\u3053\u3068\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>11<\/strong><strong>\u5e74\u751f\u306e\u4e3b\u8981\u6982\u5ff5<\/strong>\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u5b9a\u7fa9\uff1a\u5909\u6570\u304c1\u306e\u3079\u304d\u4e57\u306e\u307f\u3092\u6301\u3064\u65b9\u7a0b\u5f0f\uff08\u4f8b\uff1a<math data-latex=\"2x + 3 = 9\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x + 3 = 9<\/annotation><\/semantics><\/math>\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u30b0\u30e9\u30d5\u8868\u73fe\uff1a\u5ea7\u6a19\u5e73\u9762\u4e0a\u306b\u76f4\u7dda\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u5f62\u5f0f\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u25e6 \u50be\u304d\u30fb\u5207\u7247\uff1a <math data-latex=\"y = mx + b\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y = mx + b<\/annotation><\/semantics><\/math>\uff08 <math data-latex=\"m\"><semantics><mi>m<\/mi><annotation encoding=\"application\/x-tex\">m<\/annotation><\/semantics><\/math>= \u50be\u304d\/\u52fe\u914d\u3001 <math data-latex=\"b\"><semantics><mi>b<\/mi><annotation encoding=\"application\/x-tex\">b<\/annotation><\/semantics><\/math>= y-\u5207\u7247\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u25e6 \u6a19\u6e96\u5f62\uff1a<math data-latex=\"Ax  + By = C\"><semantics><mrow><mi>A<\/mi><mi>x<\/mi><mo>+<\/mo><mi>B<\/mi><mi>y<\/mi><mo>=<\/mo><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Ax  + By = C<\/annotation><\/semantics><\/math> \u307e\u305f\u306f <math data-latex=\"Ax + By + C = 0\"><semantics><mrow><mi>A<\/mi><mi>x<\/mi><mo>+<\/mo><mi>B<\/mi><mi>y<\/mi><mo>+<\/mo><mi>C<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">Ax + By + C = 0<\/annotation><\/semantics><\/math> \u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u4e00\u5909\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u25e6 \u624b\u9806\uff1a\u62ec\u5f27\u3092\u5c55\u958b\u3057\u3001\u540c\u985e\u9805\u3092\u30b0\u30eb\u30fc\u30d7\u5316\u3057\u3001\u7c21\u7d04\u3057\u3001\u4e21\u8fba\u3067\u9006\u6f14\u7b97\uff08\u52a0\u7b97\uff0f\u6e1b\u7b97\u3001\u4e57\u7b97\uff0f\u9664\u7b97\uff09\u3092\u4f7f\u7528\u3057\u3066\u5909\u6570\u3092\u5206\u96e2\u3057\u3001\u30d0\u30e9\u30f3\u30b9\u3092\u4fdd\u3061\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u25e6 \u4f8b\uff1a2(x + 3) = 10 \u2192 2x + 6 = 10 \u2192 2x = 4 \u2192 x = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u4e8c\u5909\u6570\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\uff08\u30b0\u30e9\u30d5\u4f5c\u6210\uff09\uff1a\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3059\uff08x, y\uff09\u306e\u30da\u30a2\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u76f4\u7dda\u4e0a\u306e\u5207\u7247\u307e\u305f\u306f\u70b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u8868\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u4e00\u6b21\u4e0d\u7b49\u5f0f\uff1a\u76f4\u7dda\u4e0a\u306e\u7bc4\u56f2\u3092\u8868\u3059\u305f\u3081\u306b\u3001= \u306e\u4ee3\u308f\u308a\u306b &lt;\u3001&gt;\u3001\u2264\u3001\u2265 \u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u5fdc\u7528\uff1a\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u3001\u8ddd\u96e2\uff0f\u6642\u9593\u3001\u8ca1\u52d9\u3001\u6df7\u5408\u554f\u984c\u306a\u3069\u306e\u73fe\u5b9f\u306e\u30b7\u30ca\u30ea\u30aa\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3001\u89e3\u304d\u307e\u3059\uff08\u554f\u984c\u89e3\u6c7a\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Year 11 <\/strong><strong>\u306e\u65b0\u6a5f\u80fd<\/strong>\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u3088\u308a\u8907\u96d1\u306a\u591a\u6bb5\u968e\u65b9\u7a0b\u5f0f<\/strong>\uff1a\u4e21\u8fba\u306b\u5909\u6570\u3068\u5b9a\u6570\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3002\u3088\u308a\u9ad8\u5ea6\u306a\u30b0\u30eb\u30fc\u30d7\u5316\u3068\u7c21\u7d04\u5316\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u5165\u9580<\/strong>\uff1a2\u3064\u4ee5\u4e0a\u306e\u9023\u7acb\u4e00\u6b21\u65b9\u7a0b\u5f0f\u3092\u540c\u6642\u306b\uff08\u4f8b\u3048\u3070\u3001\u4ee3\u5165\u6cd5\u3084\u6d88\u53bb\u6cd5\u3092\u7528\u3044\u3066\uff09\u89e3\u304d\u3001\u5171\u901a\u89e3\uff08\u4ea4\u70b9\uff09\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u30d9\u30af\u30c8\u30eb<\/strong>\uff1a\u7dda\u578b\u4ee3\u6570\u306f\u3001\u65b9\u5411\u3068\u5927\u304d\u3055\u306b\u95a2\u9023\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u304b\u3089\u59cb\u307e\u308a\u3001\u7dda\u5f62\u95a2\u4fc2\u306e\u6982\u5ff5\u3092\u62e1\u5f35\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u554f\u984c\u89e3\u6c7a\u306e\u6587\u8108<\/strong>\uff1a\u3053\u308c\u3089\u306e\u4ee3\u6570\u30b9\u30ad\u30eb\u3092\u3088\u308a\u8907\u96d1\u306a\u6587\u7ae0\u984c\u306b\u9069\u7528\u3057\u3001\u8a00\u8449\u304b\u3089\u65b9\u7a0b\u5f0f\u3078\u306e\u7ffb\u8a33\u3092\u5fc5\u8981\u3068\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">**********************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u30d9\u30af\u30c8\u30eb<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9ad8\u68211\u5e74\u751f\u306e\u6570\u5b66\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306f\u5927\u304d\u3055\uff08\u5927\u304d\u3055\uff09\u3068\u65b9\u5411\u306e\u4e21\u65b9\u3092\u6301\u3064\u91cf\u3067\u3042\u308a\u3001\u77e2\u5370\u3067\u8996\u899a\u7684\u306b\u8868\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5927\u304d\u3055\u306e\u307f\u3092\u6301\u3064\u30b9\u30ab\u30e9\u30fc\u3068\u306f\u5bfe\u7167\u7684\u3067\u3059\u3002\u751f\u5f92\u306f\u3001\u5217\u30d9\u30af\u30c8\u30eb\uff08\u4f8b\uff1a <strong> <\/strong><math data-latex=\"\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)\"><semantics><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mtable columnalign=\"center\"><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>x<\/mi><\/mtd><\/mtr><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>y<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)<\/annotation><\/semantics><\/math>  \u3084 i\/j \u8868\u8a18\u6cd5\u306a\u3069\u306e\u8868\u8a18\u6cd5\u3092\u7528\u3044\u3066\u30d9\u30af\u30c8\u30eb\u3092\u8868\u3059\u65b9\u6cd5\u3001\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u6cd5\u30fb\u6e1b\u6cd5\uff08\u982d\u304b\u3089\u5c3e\u3001\u307e\u305f\u306f\u6210\u5206\u3054\u3068\uff09\u3092\u7406\u89e3\u3059\u308b\u65b9\u6cd5\u3001\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u5927\u304d\u3055\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3001\u305d\u3057\u3066\u305d\u308c\u3089\u3092\u5909\u4f4d\u3001\u901f\u5ea6\u3001\u529b\u306b\u95a2\u3059\u308b\u554f\u984c\u306b\u9069\u7528\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3b\u8981\u6982\u5ff5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9a\u7fa9\uff1a\u30d9\u30af\u30c8\u30eb\u306f\u3001\u79fb\u52d5\u91cf\uff08\u5927\u304d\u3055\uff09\u3068\u79fb\u52d5\u5148\uff08\u65b9\u5411\uff09\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u52d5\u304d\u3084\u529b\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8868\u73fe\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6709\u5411\u7dda\u5206\uff1a\u59cb\u70b9\uff08\u5c3e\uff09\u304b\u3089\u7d42\u70b9\uff08\u982d\uff09\u306b\u5411\u304b\u3046\u77e2\u5370\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5217\u30d9\u30af\u30c8\u30eb: <strong> <\/strong><math data-latex=\"\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)\"><semantics><mrow><mo fence=\"true\" form=\"prefix\">(<\/mo><mtable columnalign=\"center\"><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>x<\/mi><\/mtd><\/mtr><mtr><mtd style=\"padding-left:0em;padding-right:0em;\"><mi>y<\/mi><\/mtd><\/mtr><\/mtable><mo fence=\"true\" form=\"postfix\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\begin{matrix}x\\\\ y\\end{matrix}\\right)<\/annotation><\/semantics><\/math>  \u306f\u3001\u6c34\u5e73\u65b9\u5411 (x) \u3068\u5782\u76f4\u65b9\u5411 (y) \u306e\u5909\u5316\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">i, j \u8868\u8a18: <math data-latex=\"xi + yj\"><semantics><mrow><mi>x<\/mi><mi>i<\/mi><mo>+<\/mo><mi>y<\/mi><mi>j<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">xi + yj<\/annotation><\/semantics><\/math>\u3001\u3053\u3053\u3067 <math data-latex=\"i\"><semantics><mi>i<\/mi><annotation encoding=\"application\/x-tex\">i<\/annotation><\/semantics><\/math>\u306f\u6c34\u5e73\u65b9\u5411\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3001 <math data-latex=\"j\"><semantics><mi>j<\/mi><annotation encoding=\"application\/x-tex\">j<\/annotation><\/semantics><\/math>\u306f\u5782\u76f4\u65b9\u5411\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5927\u304d\u3055: \u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u3002\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u7528\u3044\u3066\u6c42\u3081\u3089\u308c\u307e\u3059 (\u4f8b:  <math data-latex=\"|\\vec{v}|=\\sqrt{x^{2}+y^{2}}\"><semantics><mrow><mi>|<\/mi><mover><mi>v<\/mi><mo stretchy=\"false\" style=\"transform:scale(0.75) translate(10%, 30%);\">\u2192<\/mo><\/mover><mi>|<\/mi><mo>=<\/mo><msqrt><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>y<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">|\\vec{v}|=\\sqrt{x^{2}+y^{2}}<\/annotation><\/semantics><\/math> )\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\uff1a\u52a0\u7b97\uff1a\u5e7e\u4f55\u5b66\u7684\u306b\uff08\u982d\u304b\u3089\u5c3e\u307e\u3067\uff09\u3001\u307e\u305f\u306f\u5bfe\u5fdc\u3059\u308b\u6210\u5206\u3092\u52a0\u7b97\u3057\u307e\u3059\u3002\u6e1b\u7b97\uff1a\u52a0\u7b97\u3068\u540c\u69d8\u3001\u307e\u305f\u306f\u8ca0\u306e\u30d9\u30af\u30c8\u30eb\uff08\u53cd\u8ee2\u3057\u305f\u30d9\u30af\u30c8\u30eb\uff09\u3092\u52a0\u7b97\u3057\u307e\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\uff1a\u30d9\u30af\u30c8\u30eb\u306b\u6570\u5024\u3092\u4e57\u3058\u308b\u3068\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u304c\u5909\u5316\u3057\u307e\u3059\uff08\u4f38\u7e2e\u3057\u307e\u3059\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d9\u30af\u30c8\u30eb\u306e\u7a2e\u985e\uff1a\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\uff1a\u539f\u70b9\uff080,0\uff09\u304b\u3089\u59cb\u307e\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5909\u4f4d\u30d9\u30af\u30c8\u30eb\uff1a\u5e73\u9762\u4e0a\u306e\u4efb\u610f\u306e\u5834\u6240\u306b\u914d\u7f6e\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\uff1a\u5927\u304d\u3055\u306f1\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5fdc\u7528\uff1a\u98a8\u306e\u5f71\u97ff\u3092\u53d7\u3051\u305f\u98db\u884c\u6a5f\u306e\u5bfe\u5730\u901f\u5ea6\u3084\u3001\u7269\u4f53\u306b\u4f5c\u7528\u3059\u308b\u529b\u306a\u3069\u3001\u73fe\u5b9f\u4e16\u754c\u306e\u30b7\u30ca\u30ea\u30aa\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9ad8\u68213\u5e74\u751f\u306e\u30d9\u30af\u30c8\u30eb\u306f\u3001\u7269\u7406\u5b66\u3084\u5fae\u7a4d\u5206\u3001\u7dda\u5f62\u4ee3\u6570\u306a\u3069\u306e\u9ad8\u7b49\u6570\u5b66\u306b\u4e0d\u53ef\u6b20\u306a\u3001\u52d5\u304d\u3068\u65b9\u5411\u306e\u6982\u5ff5\u3092\u5f62\u5f0f\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u57fa\u672c\u7684\u306a\u4ee3\u6570\u304b\u3089\u3088\u308a\u9ad8\u5ea6\u306a\u6570\u5b66\u3078\u306e\u6a4b\u6e21\u3057\u3092\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*******************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u884c\u5217<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">11\u5e74\u751f\u306e\u6570\u5b66\u3067\u306f\u3001\u884c\u5217\u3068\u306f\u884c\u3068\u5217\u306b\u6574\u7406\u3055\u308c\u305f\u6570\u5b57\u3084\u8a18\u53f7\u306e\u9577\u65b9\u5f62\u306e\u914d\u5217\u3067\u3042\u308a\u3001\u79d1\u5b66\u3001\u7d4c\u6e08\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b5\u30a4\u30a8\u30f3\u30b9\u306b\u304a\u3051\u308b\u30c7\u30fc\u30bf\u306e\u8868\u73fe\u3084\u554f\u984c\u306e\u89e3\u6c7a\u306b\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u4e3b\u8981\u306a\u6982\u5ff5\u306b\u306f\u3001\u884c\u5217\u306e\u9806\u5e8f\uff082&#215;3\u306a\u3069\u306e\u6b21\u5143\uff09\u3001\u8981\u7d20\uff08\u30a8\u30f3\u30c8\u30ea\uff09\u3001\u305d\u3057\u3066\u52a0\u7b97\u3001\u6e1b\u7b97\uff08\u8981\u7d20\u3054\u3068\uff09\u3001\u4e57\u7b97\u306a\u3069\u306e\u57fa\u672c\u6f14\u7b97\u304c\u3042\u308a\u3001\u58f2\u4e0a\u3084\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3068\u3044\u3063\u305f\u73fe\u5b9f\u4e16\u754c\u306e\u30b7\u30ca\u30ea\u30aa\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e3b\u8981\u306a\u6982\u5ff5<\/strong>\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u5b9a\u7fa9\uff1a\u884c\u5217\u3068\u306f\u3001\u884c\uff08\u6c34\u5e73\uff09\u3068\u5217\uff08\u5782\u76f4\uff09\u306b\u914d\u7f6e\u3055\u308c\u305f\u6570\u5b57\u3001\u8a18\u53f7\u3001\u307e\u305f\u306f\u5f0f\u306e\u30b0\u30ea\u30c3\u30c9\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u8868\u8a18\u6cd5\uff1a\u884c\u5217\u306f\u901a\u5e38\u3001\u5927\u6587\u5b57\uff08\u4f8b\uff1aA\u3001B\uff09\u3067\u8868\u8a18\u3055\u308c\u3001\u305d\u306e\u8981\u7d20\u306f\u6dfb\u3048\u5b57\u4ed8\u304d\u306e\u5c0f\u6587\u5b57\uff08\u4f8b\uff1a <math data-latex=\"a_{ij}\"><semantics><msub><mi>a<\/mi><mrow><mi>i<\/mi><mi>j<\/mi><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">a_{ij}<\/annotation><\/semantics><\/math> . <math data-latex=\"i^{th}\"><semantics><msup><mi>i<\/mi><mrow><mi>t<\/mi><mi>h<\/mi><\/mrow><\/msup><annotation encoding=\"application\/x-tex\">i^{th}<\/annotation><\/semantics><\/math> \u884c, <math data-latex=\"j^{th}\"><semantics><msup><mi>j<\/mi><mrow><mi>t<\/mi><mi>h<\/mi><\/mrow><\/msup><annotation encoding=\"application\/x-tex\">j^{th}<\/annotation><\/semantics><\/math>\u5217\uff09\u3067\u8868\u8a18\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u9806\u5e8f\uff08\u6b21\u5143\uff09\uff1a\u884c\u5217\u306e\u30b5\u30a4\u30ba\u306f\u884c\u00d7\u5217\u3067\u8868\u3055\u308c\u307e\u3059\uff08\u4f8b\uff1a2&#215;3\u306e\u884c\u5217\u306f2\u884c3\u5217\u3067\u3059\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u8981\u7d20\uff1a\u884c\u5217\u5185\u306e\u500b\u3005\u306e\u6570\u5024\u307e\u305f\u306f\u9805\u76ee\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u57fa\u672c\u6f14\u7b97<\/strong>\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u52a0\u7b97\uff0f\u6e1b\u7b97\uff1a\u8981\u7d20\u3054\u3068\u306b\u5b9f\u884c\u3057\u307e\u3059\u3002\u884c\u5217\u306f\u540c\u3058\u9806\u5e8f\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\uff1a\u884c\u5217\u306b\u5358\u4e00\u306e\u6570\uff08\u30b9\u30ab\u30e9\u30fc\uff09\u3092\u4e57\u7b97\u3057\u307e\u3059\u3002\u5404\u8981\u7d20\u306b\u305d\u306e\u6570\u3092\u4e57\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u884c\u5217\u4e57\u7b97\uff1a\u3088\u308a\u8907\u96d1\u306a\u6f14\u7b97\u3067\u3001\u9806\u5e8f\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\uff08\u901a\u5e38\u3001AB\u306fBA\u3068\u7b49\u3057\u304f\u3042\u308a\u307e\u305b\u3093\uff09\u3002\u591a\u304f\u306e\u5fdc\u7528\u306b\u304a\u3044\u3066\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5fdc\u7528<\/strong>\uff0811\u5e74\u751f\u30ec\u30d9\u30eb\uff09\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u5b9f\u4e16\u754c\u306e\u30c7\u30fc\u30bf\u306e\u30e2\u30c7\u30ea\u30f3\u30b0\uff1a\u58f2\u4e0a\u9ad8\u3001\u30c1\u30b1\u30c3\u30c8\u8ca9\u58f2\u6570\u3001\u5728\u5eab\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u56f3\uff1a\u9053\u8def\u7db2\u3084\u901a\u4fe1\u7db2\u3092\u8a18\u8ff0\u3057\u307e\u3059\uff08\u4f8b\uff1a1\u6bb5\u968e\u63a5\u7d9a\u307e\u305f\u306f2\u6bb5\u968e\u63a5\u7d9a\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 \u554f\u984c\u89e3\u6c7a\uff1a\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u304d\u3001\u30c7\u30fc\u30bf\u3092\u52b9\u7387\u7684\u306b\u5206\u6790\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8cea\u7684\u306b\u3001\u884c\u5217\u306f\u30c7\u30fc\u30bf\u3092\u6574\u7406\u304a\u3088\u3073\u64cd\u4f5c\u3059\u308b\u305f\u3081\u306e\u69cb\u9020\u5316\u3055\u308c\u305f\u65b9\u6cd5\u3092\u63d0\u4f9b\u3057\u3001\u69d8\u3005\u306a\u5206\u91ce\u306e\u8907\u96d1\u306a\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f11\u5e74\u751f\u306e\u6570\u5b66\u306e\u91cd\u8981\u306a\u7126\u70b9\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*******************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&gt;&gt; <\/strong><strong>\u7dda\u5f62\u5909\u63db<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u7dda\u5f62\u5909\u63db\u306f\u3001\u6a19\u6e96\u7684\u306a11\u5e74\u751f\u306e\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u3067\u306f\u306a\u304f\u3001\u5927\u5b66\u30ec\u30d9\u30eb\uff08\u307e\u305f\u306fAP\u5fae\u7a4d\u5206\u5b66\u3084\u7dda\u578b\u4ee3\u6570\u306a\u3069\u306e\u9ad8\u6821\u306e\u4e0a\u7d1a\u30b3\u30fc\u30b9\uff09\u3067\u5b66\u3076\u9ad8\u5ea6\u306a\u30c8\u30d4\u30c3\u30af\u3067\u3059\u300211\u5e74\u751f\u306e\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u3067\u306f\u901a\u5e38\u3001\u4e26\u9032\u3001\u53cd\u5c04\u3001\u62e1\u5927\u7e2e\u5c0f\u3068\u3044\u3063\u305f\u95a2\u6570\u306e\u57fa\u672c\u7684\u306a\u5909\u63db\u3092\u542b\u3080\u3001\u57fa\u790e\u7684\u306a\u4ee3\u6570\u3068\u5e7e\u4f55\u5b66\u306b\u91cd\u70b9\u304c\u7f6e\u304b\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7dda\u5f62\u5909\u63db\u3068\u306f\u4f55\u304b\uff08\u305d\u3057\u3066<\/strong><strong>11<\/strong><strong>\u5e74\u751f\u3067\u306f\u6271\u308f\u306a\u3044\u3082\u306e\uff09<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7dda\u5f62\u5909\u63db\uff08\u7dda\u578b\u5199\u50cf\u307e\u305f\u306f\u7dda\u578b\u6f14\u7b97\u5b50\u3068\u3082\u547c\u3070\u308c\u308b\uff09\u306f\u3001\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u9593\u306e\u7279\u6b8a\u306a\u95a2\u6570\u3067\u3042\u308a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97\u3068\u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\u306e\u6f14\u7b97\u3092\u300c\u4fdd\u5b58\u300d\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u5f0f\u306b\u306f\u3001\u5909\u63db <math><semantics><mi>T<\/mi><\/semantics><\/math>\u304c\u7dda\u5f62\u3067\u3042\u308b\u3068\u306f\u3001\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb <math><semantics><mi>u<\/mi><\/semantics><\/math>, <math><semantics><mi>v<\/mi><\/semantics><\/math>\u304a\u3088\u3073 \u4efb\u610f\u306e\u30b9\u30ab\u30e9\u30fc <math><semantics><mi>c<\/mi><\/semantics><\/math> \u306b\u5bfe\u3057\u3066\u3001\u6b21\u306e2\u3064\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u5834\u5408\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. \u52a0\u6cd5\u6027\uff1a <math><semantics><mrow><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo>+<\/mo><mi>\ud835\udc2f<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2f<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. \u540c\u6b21\u6027\uff1a\u00a0<math><semantics><mrow><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>c<\/mi><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>c<\/mi><mi>T<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\ud835\udc2e<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u3089\u306e\u6027\u8cea\u306b\u3088\u308a\u3001\u5909\u63db\u5f8c\u3082\u3059\u3079\u3066\u306e\u76f4\u7dda\u304c\u76f4\u7dda\u306e\u307e\u307e\u3067\u3042\u308a\u3001\u539f\u70b9\u304c\u56fa\u5b9a\u3055\u308c\u305f\u307e\u307e\u3067\u3042\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4e3b\u306a\u7279\u5fb4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u884c\u5217<\/strong>\uff1a\u3059\u3079\u3066\u306e\u7dda\u5f62\u5909\u63db\u306f\u884c\u5217\u306e\u4e57\u7b97\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u56de\u8ee2\u3001\u53cd\u8ee2\u3001\u62e1\u5927\u7e2e\u5c0f\u306a\u3069\u306e\u539f\u70b9\u3092\u56fa\u5b9a\u3057\u305f\u5e7e\u4f55\u5b66\u7684\u6f14\u7b97\u306f\u7dda\u5f62\u5909\u63db\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u5e7e\u4f55\u5b66\u7684\u89e3\u91c8<\/strong>\uff1a\u8996\u899a\u7684\u306b\u306f\u3001\u7dda\u5f62\u5909\u63db\u306f\u30b0\u30ea\u30c3\u30c9\u7dda\u3092\u5e73\u884c\u304b\u3064\u7b49\u9593\u9694\u306b\u4fdd\u3061\u306a\u304c\u3089\u3001\u30b0\u30ea\u30c3\u30c9\u3092\u4f38\u7e2e\u3001\u56de\u8ee2\u3001\u307e\u305f\u306f\u305b\u3093\u65ad\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u539f\u70b9\u306f\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b<\/strong>\uff1a\u5909\u63db\u304c\u7dda\u5f62\u3067\u306a\u3044\u304b\u3069\u3046\u304b\u3092\u7c21\u5358\u306b\u78ba\u8a8d\u3059\u308b\u306b\u306f\u3001\u539f\u70b9 (0,0) \u304c\u79fb\u52d5\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u5909\u63db\u306b\u3088\u3063\u3066\u539f\u70b9\u304c\u79fb\u52d5\u3059\u308b\uff08\u4e26\u9032\u307e\u305f\u306f\u30b7\u30d5\u30c8\uff09\u5834\u5408\u3001\u6570\u5b66\u7684\u306a\u610f\u5473\u3067\u306e\u7dda\u5f62\u5909\u63db\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">11 \u5e74\u751f\u3068\u306e\u95a2\u9023\u6027<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30aa\u30fc\u30b9\u30c8\u30e9\u30ea\u30a2\u307e\u305f\u306f\u82f1\u56fd\u306e\u6a19\u6e96\u7684\u306a 11 \u5e74\u751f\u306e\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u3067\u306f\u3001\u6b21\u306e\u3088\u3046\u306a\u95a2\u6570\u306e\u5909\u63db\u306b\u906d\u9047\u3059\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u4e26\u9032<\/strong>\uff1a\u30b0\u30e9\u30d5\u3092\u4e0a\u4e0b\u5de6\u53f3\u306b\u30b7\u30d5\u30c8\u3059\u308b\u3053\u3068\uff08\u4f8b\uff1a<math><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>k<\/mi><\/mrow><\/semantics><\/math>  \u307e\u305f\u306f <math data-latex=\"f(x - h))\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mi>h<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(x &#8211; h))<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u53cd\u8ee2<\/strong>\uff1a\u8ef8\u3092\u631f\u3093\u3067\u30b0\u30e9\u30d5\u3092\u53cd\u8ee2\u3059\u308b\u3053\u3068\uff08\u4f8b\uff1a<math><semantics><mrow><mo>\u2212<\/mo><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><\/semantics><\/math> \u307e\u305f\u306f <math data-latex=\"f(\u2212x )\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">\u2212<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">f(\u2212x )<\/annotation><\/semantics><\/math>)\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2022 <strong>\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0<\/strong>\uff1a\u30b0\u30e9\u30d5\u3092\u5782\u76f4\u65b9\u5411\u307e\u305f\u306f\u6c34\u5e73\u65b9\u5411\u306b\u4f38\u7e2e\u3059\u308b\u3053\u3068\uff08\u4f8b\uff1a<math data-latex=\"af(x))\"><semantics><mrow><mi>a<\/mi><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">af(x))<\/annotation><\/semantics><\/math>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9ad8\u6821\u3067\u300c\u7dda\u5f62\u95a2\u6570\u300d\u3068\u3044\u3046\u7528\u8a9e\u306f\u901a\u5e38\u3001<math data-latex=\"f(x) = mx +b\"><semantics><mrow><mi>f<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>x<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">f(x) = mx +b<\/annotation><\/semantics><\/math> \uff08\u76f4\u7dda\uff09\u306e\u5f62\u3092\u3057\u305f\u95a2\u6570\u3092\u6307\u3057\u307e\u3059\u304c\u3001y\u5207\u7247 \u304c 0\uff08\u3064\u307e\u308a\u3001\u76f4\u7dda\u304c\u539f\u70b9\u3092\u901a\u308b\uff09\u306e\u5834\u5408\u306b\u306e\u307f\u3001\u6b63\u5f0f\u306a\u7dda\u5f62\u5909\u63db\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">*******************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Linear algebra is&nbsp;&nbsp;branch of mathematics focused on vectors, matrices, and linear equations. In Year 11 mathematics, the subject is typically an introduction to these concepts, building upon general algebra skills.&nbsp; Core Concepts Covered in Year 11 The topics introduced at this level generally form the foundations of the subject and are more computational than abstract. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1077","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1077","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1077"}],"version-history":[{"count":2,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1077\/revisions"}],"predecessor-version":[{"id":1080,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1077\/revisions\/1080"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1077"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1077"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1077"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}