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If $\mathrm{B}=\left[\begin{array}{lll}3 & 2 & 0 \\ 2 & 4 & 0 \\ 1 & 1 & 0\end{array}\right]$, then what is adjoint of B equal to?
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The correct answer is:
$\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]$
$B=\left[\begin{array}{lll}3 & 2 & 0 \\ 2 & 4 & 0 \\ 1 & 1 & 0\end{array}\right]$
C factor matrix of
$B=\left[\begin{array}{ccc}(4)(0)-(0)(1) & -[(2)(0)-(0)(1)] & (2)(1)-(4)(1) \\ -[2(0)-(0)(1)] & 3(0)-(0)(1) & -[(3)(1)-(2)(1)] \\ 2(0)-0(4) & -[3(0)-2(0)] & 3(4)-2(2)\end{array}\right]$
$=\left[\begin{array}{ccc}0 & 0 & -2 \\ 0 & 0 & -1 \\ 0 & 0 & 8\end{array}\right]$
Adjoint $B=\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]$
C factor matrix of
$B=\left[\begin{array}{ccc}(4)(0)-(0)(1) & -[(2)(0)-(0)(1)] & (2)(1)-(4)(1) \\ -[2(0)-(0)(1)] & 3(0)-(0)(1) & -[(3)(1)-(2)(1)] \\ 2(0)-0(4) & -[3(0)-2(0)] & 3(4)-2(2)\end{array}\right]$
$=\left[\begin{array}{ccc}0 & 0 & -2 \\ 0 & 0 & -1 \\ 0 & 0 & 8\end{array}\right]$
Adjoint $B=\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 0 \\ -2 & -1 & 8\end{array}\right]$
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