Question

The minors of $-4$ and $9$ and the cofactors of $-4$ and 9 in matrix $\left[\begin{array}{ccc}-1& -2& 3\\ -4& -5& -6\\ -7& 8& 9\end{array}\right]$ 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 $=\left[\begin{array}{ccc}-1& -2& 3\\ -4& -5& -6\\ -7& 8& 9\end{array}\right]$ minor of
$(-4)=\left|\begin{array}{cc}-2& 3\\ 8& 9\end{array}\right|$
$=-18-24=-42$ minor of
$9=\left|\begin{array}{cc}-1& -2\\ -4& -5\end{array}\right|$
$=5-8=-3$ cofactor of
$(-4)={(-1)}^{2+1}\left|\begin{array}{cc}-2& 3\\ 8& 9\end{array}\right|=42$
and cofactor of
$9={(-1)}^{3+3}\left|\begin{array}{cc}-1& -2\\ -4& -5\end{array}\right|=-3$