1. Tardigrade
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  3. Mathematics
  4. If f(x)=x2-5x,A=[ beginmatrix 3 1 -1 2 endmatrix ], then f(A) =

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Q. If $ f(x)={{x}^{2}}-5x,A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right], $ then $ f(A) $ =

J & K CETJ & K CET 2008Matrices

Solution:

Given $ A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right] $
$ \therefore $ $ f(A)=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right]\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right]-5\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right] $
$ =\left[ \begin{matrix} 8 & 5 \\ -5 & 3 \\ \end{matrix} \right]-\left[ \begin{matrix} 15 & 5 \\ -5 & 10 \\ \end{matrix} \right] $ $ =\left[ \begin{matrix} -7 & 0 \\ 0 & -7 \\ \end{matrix} \right] $