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

Question

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

Answer 1

 we have A = \(\begin{bmatrix} 2&3 \\ 1& 2 \end{bmatrix}\) and f(x) = x² - 4x + 1.

Therefore, f(A) = A² − 4A + I , where = \(\begin{bmatrix} 1&0 \\ 0& 1 \end{bmatrix}\) is an identity matrix of order 2.

Hence, f(A) = 0, where 0 is zero matrix of order 2.