Matrix

Question 1

Matrice Multiplication Rules

Answer 1

example

Question 2

Operation Rules

Answer 2

Question 3

Square Matrice can multiply only if….

Answer 3

Question 4

A matrice has an inverse matrice if only…

Answer 4

From colum idea,they don’t linear relevant in each column.

Or it doesn’t exist A*x=0.

Why?
Because A*x indicates x=0 but actually there are other solutions for x.

Question 5

When will we introduce Gauss-Jordan’s idea to get inverse matrice ?

Answer 5

Question 6

How to get inverse matrice: Gauss-Jordan’s idea

Firstly

Answer 6

Then we get I matrice on the left side

Question 7

What’s the meaning of upper triangle matrix?

Answer 7

Upper triangular matrices have some nice properties. For example, they are straightforward to solve in systems of linear equations. Since there are no coefficients below the diagonal, we can use back-substitution to find the values of the unknown variables easily.

Additionally, the determinant of an upper triangular matrix is simply the product of its diagonal elements. This property makes computing determinants of upper triangular matrices relatively simple compared to general matrices.

Question 8

矩阵公式总结 ：

Answer 8

Question 9

什么是逆矩阵？逆矩阵的规律？

Answer 9

Question 10

如何用定义法求逆矩阵？

Answer 10

2x2 矩阵 伴随矩阵 的规律：主对角线对调，副对线 前面加一个 “-”

Question 11

有关 抽象逆矩阵的题目 ：

Answer 11

Question 12

有关抽象逆矩阵的题目 ：

hint ：构造题目要求的

Answer 12

Question 13

例题 ：分块矩阵的计算

Answer 13

Question 14

求分块矩阵的逆矩阵的规律？

Answer 14

Question 15

例题 ：计算分块矩阵的逆矩阵

Answer 15

Question 16

2x2 矩阵 伴随矩阵 的规律：主对角线对调，副对线 前面加一个 “-”

Answer 16

Question 17

计算 常见矩阵（2x2 & 3x 3 矩阵）伴随矩阵 的方法

2x2 矩阵 伴随矩阵 的规律：主对角线对调，副对线 前面加一个 “-”

ps：图片显示的是求3x3矩阵

Answer 17

Question 18

特殊矩阵 归纳 ：

Answer 18

单位矩阵也可以叫 I

Question 19

例题 ： 矩阵运算（利用运算顺序可交换）

Answer 19

Question 20

例题 ： 利用逆矩阵计算 A*x = B

Answer 20

Question 21

例题 ：分块矩阵计算矩阵n次方

Answer 21