📚 Matrices and Systems of Linear Equations in Edexcel FP1 | Edexcel FP1 矩阵与线性方程组
In Edexcel Further Maths Core Pure 1, matrices are used to solve simultaneous linear equations and to describe linear transformations of vectors. This topic combines algebraic manipulation, geometric interpretation, and careful attention to order. This article reviews the essential definitions, methods, common misconceptions, and exam strategies for the matrix and linear-systems content in Core Pure 1.
在 Edexcel 进阶数学 Core Pure 1 中，矩阵被用来解联立线性方程组，并描述向量的线性变换。该主题结合了代数运算、几何解释以及对顺序的严格关注。本文回顾 Core Pure 1 中矩阵与线性方程组的核心定义、解题方法、常见误区以及考试策略。
1. Matrix Basics and Terminology | 矩阵基础与术语
matrix is written as m × n, where m is the number of rows and n is the number of columns.
矩阵是由数字按照行和列排列成的矩形阵列。矩阵的阶数写作 m × n，其中 m 是行数，n 是列数。
Two matrices can be added or subtracted only if they have the same order. Addition and subtraction are performed entry by entry. Scalar multiplication multiplies every entry by a constant.
两个矩阵只有在阶数相同时才能相加或相减。加法和减法是对应元素逐一进行。标量乘法则是将常数乘以矩阵中的每一个元素。
trix A, AI = IA = A. The zero matrix O has every entry equal to 0 and satisfies A + O = A.
2×2 单位矩阵为 I = [1 0; 0 1]。对于任何 2×2 矩阵 A，都有 AI = IA = A。零矩阵 O 的每一个元素都是 0，并且满足 A + O = A。
2. Matrix Multiplication | 矩阵乘法
lumns of A equals the number of rows of B. If A is m × n and B is n × p, then AB is m × p.
两个矩阵 A 和 B 只有在前者的列数等于后者的行数时才能相乘。如果 A 是 m × n 矩阵，B 是 n × p 矩阵，那么 AB 是 m × p 矩阵。
f the first matrix by each column of the second matrix. In general, matrix multiplication is not commutative, so AB ≠ BA in most cases.
对于 2×2 矩阵，用第一个矩阵的每一行分别乘以第二个矩阵的每一列。一般地，矩阵乘法不满足交换律，因此在大多数情况下 AB ≠ BA。
= [1 2; 3 4] and B = [5 6; 7 8], then AB = [(1)(5)+(2)(7) (1)(6)+(2)(8); (3)(5)+(4)(7) (3
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