Given : A = \(
\begin{bmatrix}
3 & 4 \\[0.3em]
-4& -3 \\[0.3em]
\end{bmatrix}\), and f(x) = x2 – 5x + 7.
Matrix A is of order 2 x 2.
To find : f(A)
Formula used :
Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj
A2 is a matrix of order 2 x 2.
f(x) = x2 – 5x + 7
f(A) = A2 – 5A + 7I
A2 = \(
\begin{bmatrix}
-7& 0 \\[0.3em]
0 & -7 \\[0.3em]
\end{bmatrix}\)
f(A) = A2 – 5A + 7I
f(A) = A2 – 5A + 7I = \(
\begin{bmatrix}
-15& -20 \\[0.3em]
20 & 15 \\[0.3em]
\end{bmatrix}\)
f(A) = A2 – 5A + 7I = \(
\begin{bmatrix}
-15& -20 \\[0.3em]
20 & 15 \\[0.3em]
\end{bmatrix}\)