Page 74 - DMTH201_Basic Mathematics-1

Unit 3: Matrix

Notes
2 4 6 4 8 16
2A 2B 8 14 10 0 12 6
0 16 20 10 14 22

2 4 4 8 6 16
8 0 14 12 10 6
0 10 16 14 20 22

2 4 22
2A 2B 8 26 4 ...(2)
10 30 42

From (1) and (2), 2(A B ) 2A 2 .
B
0 1 1 0 2 2
Example: If A , B , prove that A B 2I 0.
1 0 0 1
Solution:

0 1 0 1 0 1 0 0 1 0
A 2
1 0 1 0 0 0 1 0 0 1

1 0 1 0 1 0 0 0 1 0
B 2
0 1 0 1 0 0 0 1 0 1

1 0 2 0
2I 2
0 1 0 2

1 0 1 0 2 0
Adding, A 2 B 2 2I
0 1 0 1 0 2

1 1 2 0 0 0 0 0
0 0 0 1 1 2 0 0

A 2 B 2 2I 0.

x 2 3 4 4
Example: Solve for x, y, z given that y 4 5 6 5
z 7 8 9 6

Solution:

x 2 3 4 4
y 4 5 6 5
z 7 8 9 6

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