Page 68 - DMTH201_Basic Mathematics-1

Unit 3: Matrix

Notes
2 2 1 1
Example: If A , B find AB and BA .
2 2 1 1
Solution:

2 2 1 1
AB
2 2 1 1

2(1) ( 2)(1) 2(1) ( 2)1
2(1) 2(1) ( 2)1 2(1)

2 2 2 2 0 0
2 2 2 2 0 0

1 1 2 2
BA
1 1 2 2

1(2) 1( 2) 1( 2) 1(2)
1(2) 1( 2) 1( 2) 1(2)

2 2 2 2 0 0
2 2 2 2 0 0

1 1 1 0
Example: Simplify:
2 3 0 8
Solution:

1 1 1 0
2 3 0 8

1( 1) ( 1)0 1(0) ( 1)( 8)
( 2)( 1) ( 3)0 ( 2)(0) ( 3)( 8)

1 0 0 8 1 8
2 0 0 24 2 24

x 2 3 4
Example: Find x and y if
y 4 5 1
Solution:

x 2(4) 3( 1) 8 3 5
y 4(4) 5( 1) 16 5 11

Equating the corresponding elements, we get
x 5, y 11.

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