For the matrix $\mathrm{A}=\left[\begin{array}{ccc}2 & 0 & -1 \ 3 & 1 & 2 \ -1 & 1 & 2\end{array} ight]$, the matrix of cofactors is

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For the matrix $\mathrm{A}=\left[\begin{array}{ccc}2 & 0 & -1 \ 3 & 1 & 2 \ -1 & 1 & 2\end{array}ight]$, the matrix of cofactors is

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{A}_{11}=(-1)^{1+1}\left|\begin{array}{ll}1 & 2 \ 1 & 2\end{array}ight|=1(0)=0 \ & \mathrm{~A}_{12}=(-1)^{1+2}\left|\begin{array}{cc}3 & 2 \ -1 & 2\end{array}ight|=(-1)(8)=-8 \ & \mathrm{~A}_{13}=(-1)^{1+3}\left|\begin{array}{cc}3 & 1 \ -1 & 1\end{array}ight|=(1)(4)=4 \ & \mathrm{~A}_{21}=(-1)^{2+1}\left|\begin{array}{cc}0 & -1 \ 1 & 2\end{array}ight|=(-1)(1)=-1 \ & \mathrm{~A}_{22}=(-1)^{2+2}\left|\begin{array}{cc}2 & -1 \ -1 & 2\end{array}ight|=(1)(3)=3 \ & \mathrm{~A}_{23}=(-1)^{2+3}\left|\begin{array}{cc}2 & 0 \ -1 & 1\end{array}ight|=(-1)(2)=-2 \ & \mathrm{~A}_{31}=(-1)^{3+1}\left|\begin{array}{cc}0 & -1 \ 1 & 2\end{array}ight|=(1)(1)=1 \ & \mathrm{~A}_{32}=(-1)^{3+2}\left|\begin{array}{cc}2 & -1 \ 3 & 2\end{array}ight|=(-1)(7)=-7 \ & \mathrm{~A}_{33}=(-1)^{3+3}\left|\begin{array}{ll}2 & 0 \ 3 & 1\end{array}ight|=(1)(2)=2\end{aligned}$ $	herefore \quad$ The matrix of the cofactors is $\left[\begin{array}{ccc}0 & -8 & 4 \ -1 & 3 & -2 \ 1 & -7 & 2\end{array}ight]$ :

For the matrix $\mathrm{A}=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$,…

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