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Question

Suppose a Matrix A satisfies A2−5A+7I=0 If A5=aA+bI, then the values of 2a + b is.

A
-87
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B
-105
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C
1453
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D
1155
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Solution

The correct option is A -87
A3=AA2=A(5A7I)=5A27A=5(5A7I)7A=18A35IA4=A.A3=A(18A35I)=18(5A7I)35AA5=149A385I=55A126IA5=149A385Ia=149,b=385

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