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NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

If $A = [00 am p; 5 am p; 0]$ and $f (x) = 1 + x + x^{2} + \dots + x^{16}$ , then $f (A) =$

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Explanation

Here, $f (x) = 1 + x + x^{2} + \dots + x^{16}$

So, $f (A) = I + A + A^{2} + \dots + A^{16}$

$A^2 =  \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$

$A^{2} = A^{3} = \dots = A^{16} = 0$

So, $f (A) = I + A + A^{2} + \dots + A^{16}$

Choose the correct answer:

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