Matrices for GCSE WJEC Mathematics: Exam Focus | GCSE WJEC 数学：矩阵 考点精讲

📚 Matrices for GCSE WJEC Mathematics: Exam Focus | GCSE WJEC 数学：矩阵 考点精讲

Matrices are a crucial topic in the WJEC GCSE Mathematics Higher Tier specification. They provide a powerful way to organise data and perform transformations, and mastering them can give you a significant advantage in the exam. This article covers all key concepts: from basic operations to using inverse matrices for solving simultaneous equations and applying transformation matrices for reflections, rotations and enlargements.

矩阵是 WJEC GCSE 数学高年级考试的一个重要主题。它们提供了一个组织数据和进行变换的强大工具，掌握矩阵知识能让你在考试中占得先机。本文涵盖所有关键概念：从基本运算到利用逆矩阵解联立方程，以及运用变换矩阵进行反射、旋转和放大。

1. What is a Matrix and Its Order? | 什么是矩阵及其阶？

A matrix is a rectangular array of numbers arranged in rows and columns. The order (or dimension) of a matrix is given as rows × columns. For instance, a matrix with 2 rows and 3 columns has order 2 × 3. We usually denote matrices by bold capital letters, such as A, B, C.

矩阵是由数字排成的矩形阵列，按行和列排列。矩阵的阶（或维数）表示为 行数 × 列数。例如，一个拥有 2 行 3 列的矩阵是 2 × 3 阶的。我们通常用粗体大写字母表示矩阵，例如 A、B、C。

Each number inside a matrix is called an element or entry. The element in the i-th row and j-th column is often written as a_i,j. For example, matrix A = [2 −1; 0 5] is a 2 × 2 matrix. Its elements are a₁₁ = 2, a₁₂ = −1, a₂₁ = 0 and a₂₂ = 5. The semi-colon separates the rows.

矩阵中的每个数字称为元素。第 i 行第 j 列的元素常记为 a_i,j。例如，矩阵 A = [2 −1; 0 5] 是一个 2 × 2 矩阵，其元素为 a₁₁ = 2, a₁₂ = −1, a₂₁ = 0, a₂₂ = 5。分号用于分隔不同的行。

2. Matrix Addition and Subtraction | 矩阵的加减法

Matrices can be added or subtracted only if they have the same order. You simply add or subtract the corresponding elements. For example, if A = [4 3; 2 1] and B = [1 0; −2 3], then A + B = [4+1 3+0; 2+(−2) 1+3] = [5 3; 0 4].

只有相同阶的矩阵才能相加或相减，然后直接对对应元素进行加减。例如，若 A = [4 3; 2 1] 且 B = [1 0; −2 3]，则 A + B = [4+1 3+0; 2+(−2) 1+3] = [5 3; 0 4]。

Subtraction works identically: A − B = [4−1 3−0; 2−(−2) 1−3] = [3 3; 4 −2].

减法同理：A − B = [4−1 3−0; 2−(−2) 1−3] = [3 3; 4 −2]。

3. Scalar Multiplication (Multiplying by a Number) | 标量乘法（乘以一个数）

When a matrix is multiplied by a scalar (a single number), every element is multiplied by that scalar. If k = 3 and M = [2 −1; 0 4], then 3M = [

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