Question

The minors of - 4 and 9 and the co-factors 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, 3 ; – 42, 3
• B. –42, –3 ; 42, –3
• C. 42, 3 ; – 42, – 3
• D. 42, 3; 42, 3

Answer 1

The correct option is B

–42, –3 ; 42, –3

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