Q20 of 74 Page 7

If A = find x and y such A2 – xA + yI = O. Hence, evaluate A – 1.

A =


A2 =


=


Now, A2 – xA + yI =


= 22 – 4x + y = 0 or 4x – y = 22


= 18 – 2x = 0 or X = 9


= Y = 14


So, A2 – 5A + 7I = 0


Multiply by A – 1 both sides


= A.A. A – 1 – 9A. A – 1 + 14I. A – 1 = 0


= A – 9I + 14 A – 1 = 0


= A – 1 =


= A – 1 =


= A – 1 =


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