If A = [(2,3)(1,2)] and f(x) = x^2 – 4x + 1, find f(A).

Question

If A = \( \begin{bmatrix} 2 & 3 \\[0.3em] 1& 2 \end{bmatrix}\)and f(x) = x² – 4x + 1, find f(A).

A = [(2,3)(1,2)]

Answer 1

Given, A = \( \begin{bmatrix} 2 &3 \\[0.3em] 1 & 2 \\[0.3em] \end{bmatrix}\)

f(x) = x² – 4x + 1,

f(A) = A² – 4A + I,

f(A) = \( \begin{bmatrix} 0 &0 \\[0.3em] 0& 0 \\[0.3em] \end{bmatrix}\)