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If A = \( \begin{bmatrix} 3& 4 \\[0.3em] -4& -3 \\[0.3em] \end{bmatrix},\) find f(A), where f(x) = x2 – 5x + 7.

A = [(3,4)(-4,-3)]

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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 = \( \begin{bmatrix} -15& -20 \\[0.3em] 20 & 15 \\[0.3em] \end{bmatrix}\)

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