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Question Number 89422 by naka3546 last updated on 17/Apr/20

Commented by jagoll last updated on 17/Apr/20

$$f\left(x\right)=(x+2)(x+1)$$$$f\left(A\right)=(A+2I)(A+I)$$$$$$

Answered by som(math1967) last updated on 17/Apr/20

$$f\left(A\right)=A^2+3A+2I$$$$=\left[\begin{array}{cc}1& -2\\ 2& -1\end{array}\right]\left[\begin{array}{cc}1& -2\\ 2& -1\end{array}\right]+3\left[\begin{array}{cc}1& -2\\ 2& -1\end{array}\right]$$$$+2\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$$$=\left[\begin{array}{cc}-3& 0\\ 0& -3\end{array}\right]+\left[\begin{array}{cc}3& -6\\ 6& -3\end{array}\right]+\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$$$$=\left[\begin{array}{cc}-3+3+2& 0-6+0\\ 0+6+0& -3-3+2\end{array}\right]$$$$=\left|\begin{array}{cc}2& -6\\ 6& -4\end{array}\right|....ansB$$

Commented by naka3546 last updated on 17/Apr/20

$$thankyou$$

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