Page 72 - DMTH201_Basic Mathematics-1

Unit 3: Matrix

Notes
a h g x
Example: Find the product of A [x y z ], B h b f ,C y .
g f c z
Solution:

A is a matrix of order 1 3, B is of 3 3 and C is of 3 1.

ABC will be a matrix of order 1 1.

a h g
AB [x y z ] 1 3 h b f
g f c
3 3
ax hy gz hx by fz gx fy cz
1 3

x
(AB )C ax hy gz hx by fz gx fy cz y
z

(ax hy gz ) x (hx by fz )y (gx fy cz )z

[ax 2 hxy gzx hxy by 2 fyz gzx fyz cz 2 ]

[ax 2 by 2 cz 2 2hxy 2 fyz 2gzx ] 1 1

1 2 2
Example: If A 2 1 2 , prove that A 2 4A 5I 0.
2 2 1

Solution:
1 2 2 1 2 2
A 2 2 1 2 2 1 2
2 2 1 2 2 1

1 4 4 2 2 4 2 4 2
2 2 4 4 1 4 4 2 2

2 4 2 4 2 2 4 4 1

9 8 8
A 2 8 9 8
8 8 9

4 8 8
4A 8 4 8
8 8 4

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