Matrix Arithmetic | 矩阵运算基础

📚 Matrix Arithmetic | 矩阵运算基础

A matrix is one of the most powerful tools in A-Level Mathematics. It is a compact way of storing and manipulating data, and matrix arithmetic provides the rules for adding, subtracting and multiplying these arrays.

矩阵是 A-Level 数学中最强大的工具之一。它以一种紧凑的方式存储和操作数据，而矩阵运算则提供了对这些数表进行加、减、乘的规则。

1. What Is a Matrix? | 什么是矩阵？

A matrix is a rectangular array of numbers written inside square brackets. Each number in the matrix is called an element or entry.

矩阵是用方括号括起来的一个矩形数阵。矩阵中的每个数字称为元素或元。

A matrix is usually named with a capital letter, such as A, B or M. Its size is called its order and is given as rows × columns. For example, a 2 × 3 matrix has two rows and three columns.

矩阵通常用大写字母表示，例如 A、B 或 M。矩阵的大小称为“阶”，写作“行 × 列”。例如，一个 2 × 3 矩阵有 2 行 3 列。

The entry in row i and column j is often written as aᵢⱼ. This notation is useful when we describe rules that work for any matrix.

第 i 行第 j 列的元素通常记为 aᵢⱼ。在描述适用于任意矩阵的规则时，这种记号非常方便。

For example, the following matrix A has order 2 × 3, and its entry a₂₃ = 6.

例如，下面的矩阵 A 的阶为 2 × 3，且其元素 a₂₃ = 6。

A = [ 1 4 2 ; 3 0 6 ]

Always check the order of a matrix carefully. A 2 × 3 matrix is not the same as a 3 × 2 matrix.

一定要仔细判断矩阵的阶。2 × 3 矩阵与 3 × 2 矩阵并不相同。

2. Matrix Addition and Subtraction | 矩阵的加法与减法

Two matrices can be added or subtracted only when they have the same order. The operation is carried out element by element.

两个矩阵只有在阶数相同时才能相加或相减。运算是逐元素进行的。

If A = [aᵢⱼ] and B = [bᵢⱼ], then the entry of A + B in row i and column j is aᵢⱼ + bᵢⱼ, and the entry of A − B is aᵢ

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）