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If A = \(\begin{bmatrix} -1 & 2 \\[0.3em] 3& 1 \\[0.3em] \end{bmatrix},\) find f(A), where f(x) = x2 – 2x + 3.

A = [(-1,2)(3,1)]

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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 = \(\begin{bmatrix} 12 & -4 \\[0.3em] -6 &8 \\[0.3em] \end{bmatrix}\)

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