Question

The minors and cofactors of -4 and 9 in determinant $\left|\begin{array}{ccc}-1& -2& 3\\ -4& -5& -6\\ -7& 8& 9\end{array}\right|$ are respectively

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

Answer 1

The correct option is B $-42,42;-3,-3$

Minor of -4 is $\left|\begin{array}{cc}-2& 3\\ 8& 9\end{array}\right|=-42$
Cofactor of -4 is ${(-1)}^{1+2}\left(42\right)=42$
Minor of 9 is $\left|\begin{array}{cc}-1& -2\\ -4& -5\end{array}\right|=-3$
Cofactor of 9 is ${(-1)}^{3+3}.\left(3\right)=-3$