If f(x) = x2 - 4x + 1 , find f(A) when A = [2 3 ] first row and - Maths - Matrices

Question

If f(x) = x2 - 4x + 1 , find f(A) when A = [2 3 ] first row and
[ 1 2] second row , here x2 is x to the power of 2 or x square

Ankush Jain · Accepted Answer

Given f(x) = x2- 4x + 1 and A = $[\begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix}]$ So, f(A) = $[\begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix}]$ $[\begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix}]$ - 4 $[\begin{matrix} 2 & 3 \\ 1 & 2 \end{matrix}]$ + 1 $= [\begin{matrix} 4 + 3 & 6 + 6 \\ 2 + 2 & 3 + 4 \end{matrix}] + [\begin{matrix} - 8 & - 12 \\ - 4 & - 8 \end{matrix}] + [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 & 12 \\ 4 & 7 \end{matrix}] + [\begin{matrix} - 8 & - 12 \\ - 4 & - 8 \end{matrix}] + [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 - 8 + 1 & 12 - 12 + 0 \\ 4 - 4 + 0 & 7 - 8 + 1 \end{matrix}] = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}] = 0$

If f(x) = x2 - 4x + 1 , find f(A) when A = [2 3 ] first row and [ 1 2] second row , here x2 is x to the power of 2 or x square.