Page 70 - DMTH201_Basic Mathematics-1

Unit 3: Matrix

Notes
3 1
5 2 1
Example: If A , B 4 7
0 7 1
1 1
Verify that (AB ) B A .

Solution:

5 0
3 4 1
A 2 7 , B
1 7 1
1 1

3 1
5 2 1
AB 4 7
0 7 1
1 1

5( 3) 2(4) ( 1)1 5(1) 2(7) ( 1)( 1)

0( 3) 7(4) 1(1) 0(1) 7(7) 1( 1)

15 8 1 5 14 1

0 28 1 0 49 1

8 20
AB
29 48

8 29
(AB ) ...(1)
20 48

5 0
3 4 1
B A 2 7
1 7 1
1 1
( 3)5 4(2) 1( 1) ( 3)0 4(7) 1(1)

1(5) 7(2) ( 1)(1) 1(0) 7(7) ( 1)1

15 8 1 0 28 1

5 14 1 0 49 1

8 29
B A ...(2)
20 48

From (1) and (2), (AB ) B A

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