Page 69 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
0 2
Example: If A , prove that A 2 4I 0 where I is the unit matrix of second
2 0
order.
Solution:

0 2 0 2
A 2
2 0 2 0

0 4 0 0
A 2
0 0 4 0

4 0
A 2
0 4

1 0 4 0
4I 4
0 1 0 4

4 0 4 0
2
A 4I
0 4 0 4
4 4 0 0 0 0
0
0 0 4 4 0 0

A 2 4I 0.

3 1
Example: If A , prove that A 2 8A 13I . 0
2 5

Solution:
3 1 3 1 9 2 3 5 11 8
A 2
2 5 2 5 6 10 2 25 16 27

3 1 24 8
8A 8
2 5 16 40

1 0 13 0
13I 13
0 1 0 13

11 8 24 8 13 0
Adding, A 2 8A 13I
16 27 16 40 0 13

11 24 13 8 8 0 0 0
16 16 0 27 40 13 0 0

A 2 8A 13I 0.

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