MM_F5_4 Matrices_3

两个 matrices 相乘 28/4/2020

4.5 Multiplication of Two Matrices

1.  5 3212  1103
4

**做法:一样上一堂课的乘法**
（先横线，后直线）

5 (2) = 10 加起来
3 (1) = 3
 5 3  2 
4 2 1 13

4 (2) = 8 加起来
2 (1) = 2

10

2.  2 12  2 43   3 1181
3 1  4


2 (–2) = –4 加起来

 2 1  2 4  1 (1) = 1
3 2 1 3 –3

2 (4) = 8 加起来
1 (3) = 3

11

3 (–2) = –6 加起来

 2 1  2 4  2 (1) = 2
3 2 1 3 –4

3 (4) = 12 加起来

2 (3) = 6

18

3.  0 21 2  
3 4

4.  71 22 53 

5.  3 42 12 
3

6.  1 1213 23 
5

7.  4  32 4 2  
0  3 3

8.  1 23 3 21 
4 3

9.  1 11 4 12  
2 4
3

10.  5 1  3 43 
 1 2 3
3

4.6 Identity Matrices, I   1 0 
0 1

10 10 is an identity matrix of order 2 X 2.

1 0 0
0 1 0
 0 0 1 is an identity matrix of order 3 X 3.

4.7 Inverse Matrices

P   2 14  Q   4 21
7 7

PQ   2 14  4 21
7 7

  1 10
0

QP   4 21 2 1 
7 7 4

  1 0 
0 1

如果两个 matrices 相乘，得到的答案是  1 10 ，那么,
0

P is the inverse matrix of Q, P  Q1

Q is the inverse matrix of P, Q  P1

HOW TO find the Inverse of a Matrix

If matrix A   a b  , then its inverse A1  ad 1 bc  d b  .
c d  c a

* Determinant of a matrix = ad  bc

* If ad  bc  0, then 1 is not defined. This means matrix A
ad  bc

does not have an inverse.

1. Find the inverse matrix of  4 2  .
3 2

1. 先标上 a, b, c, d

 ab  a4 b2
c3 d 2
Inverse matrix of  4 22  4 2
3 3 2
c d

写成分数: 1  1  2 42 2. 算出：ad – bc
2 2 3

ad  bc  4(2)  2(3)  2

  1 1  3. 写成分数： ad 1 bc
  
 3 
 2 2

4. a 和 d 交换位子

b 和 c 乘 negative

 d ab 
c

5. 乘法

6.

 ab
4 d12
2. Find the inverse matrix of 6
c
ad  bc  (4)(2) 1(6)

Inverse matrix of  4 1  2
6 2
a 和 d 交换位子
写成分数: 1 1   2  14  b 和 c 乘 negative
2 2  6 


  1  1 
  3 2 
2

3. Find the inverse matrix of  3 16 
1

4. Find the inverse matrix of  3 4 
1 2

5. Find the inverse matrix of  3 2 
6 5

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