Question

If A=[31−12], show that A2−5A+7I=0, use the result to find A4.

Answer 1

A2-5A+71=0

given:

A=[31-12]

to prove:

A4

Prove

(31-12*2)-(5*31-12)+71

(19*2)-(5*19)+71

38-95+71

38-24

14

A4=(31-12)*4

A4=(19*4)

76