Question

The minors of $ -4 $ and $ 9 $ and the cofactors of $ -4 $ and 9 in matrix $ \left[ \begin{matrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \\ \end{matrix} \right] $ are respectively

• A. $ 42,3,-42,3 $
• B. $ -42,-3,42 $
• C. $ 42,3,42,3,-3 $
• D. $ 42,3,-42,-3 $

Answer 1

Answer: (B)

Given, matrix $ =\left[ \begin{matrix} -1 & -2 & 3 \\ -4 & -5 & -6 \\ -7 & 8 & 9 \\ \end{matrix} \right] $ minor of
$ (-4)=\left| \begin{matrix} -2 & 3 \\ 8 & 9 \\ \end{matrix} \right| $
$ =-18-24=-42 $ minor of
$ 9=\left| \begin{matrix} -1 & -2 \\ -4 & -5 \\ \end{matrix} \right| $
$ =5-8=-3 $ cofactor of
$ (-4)={{(-1)}^{2+1}}\left| \begin{matrix} -2 & 3 \\ 8 & 9 \\ \end{matrix} \right|=42 $
and cofactor of
$ 9={{(-1)}^{3+3}}\left| \begin{matrix} -1 & -2 \\ -4 & -5 \\ \end{matrix} \right|=-3 $