If A = begin{bmatrix} 2 & -3 -4 & 1 end{bmat | vedclass

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(C) Given $A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} \beg

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$\begin{bmatrix} 51 & 63 \ 84 & 72 \end{bmatrix}$

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(C) Given $A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix}$.First,calculate $A^2 = A 	imes A = \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 4+12 & -6-3 \ -8-4 & 12+1 \end{bmatrix} = \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix}$.Now,calculate $3A^2 = 3 \begin{bmatrix} 16 & -9 \ -12 & 13 \end{bmatrix} = \begin{bmatrix} 48 & -27 \ -36 & 39 \end{bmatrix}$.Calculate $12A = 12 \begin{bmatrix} 2 & -3 \ -4 & 1 \end{bmatrix} = \begin{bmatrix} 24 & -36 \ -48 & 12 \end{bmatrix}$.Let $M = 3A^2 + 12A = \begin{bmatrix} 48+24 & -27-36 \ -36-48 & 39+12 \end{bmatrix} = \begin{bmatrix} 72 & -63 \ -84 & 51 \end{bmatrix}$.The adjoint of a $2 	imes 2$ matrix $\begin{bmatrix} a & b \ c & d \end{bmatrix}$ is $\begin{bmatrix} d & -b \ -c & a \end{bmatrix}$.Therefore,$	ext{adj}(M) = \begin{bmatrix} 51 & 63 \ 84 & 72 \end{bmatrix}$.

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$,then $\text{adj}(3A^2 + 12A) = \dots$

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