Given : A = \(\begin{bmatrix}
-1 & 2 \\[0.3em]
3 & 1 \\[0.3em]
\end{bmatrix},\) and f(x) = x2 – 2x + 3.
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 – 2x + 3
f(A) = A2 – 2A + 3I
f(A) = A2 – 2A + 3I
f(A) = A2 – 2A + 3I = \(\begin{bmatrix}
12 & -4 \\[0.3em]
-6 &8 \\[0.3em]
\end{bmatrix}\)
f(A) = A2 – 2A + 3I = \(\begin{bmatrix}
12 & -4 \\[0.3em]
-6 &8 \\[0.3em]
\end{bmatrix}\)