Question

Let A = [2 3] and f(x) = x^2 -4x+7. [-1 2]Show that f(A)=0^2x2. Use this result to find A^5? It is a matrix question please explain

Answer 1

A=[{2,3},{-1,2}]
f(A)=A^2-4A+7I
// I is the identity matrix
A^2=[{1,12},{-4,1}]
//calculate it
f(A)=A^2-4A+7I=0
0^2*2=0=f(A)

A^2-4A+7I=0
=> A^2=4A-7I
A^5=(A^2)(A^2)(A)
4A-7I=[{1,12},{-4,1}]
A^5=[{1,12},{-4,1}] [{1,12},{-4,1}]
[{2,3},{-1,2}]
=[{-118,-93},{31,-118}]

The way i see it, it is a matrix problem

Answer 2

hence prove

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