Question

Find the minors and cofactors of elements$a_{23},a_{32}\mathrm{and}{a}_{13}$of matrix $A=\left(a_{\mathrm{ij}}\right]=\left(\begin{array}{ccc}5& 6& 7\\ 5& 2& 3\\ 4& 8& 9\end{array}\right].$

• A. $M_{23},M_{32,}{M}_{13}=16,-20,32C_{23},C_{32,}{C}_{13}=-16,20,32$
• B. $M_{23},M_{32,}{M}_{13}=16,-20,32C_{23},C_{32,}{C}_{13}=-16,20,-32$
• C. $M_{23},M_{32,}{M}_{13}=16,-20,-32C_{23},C_{32,}{C}_{13}=-16,20,32$
• D. $M_{23},M_{32,}{M}_{13}=16,-20,32C_{23},C_{32,}{C}_{13}=-16,-20,32$

Answer 1

The correct option is A $M_{23},M_{32,}{M}_{13}=16,-20,32C_{23},C_{32,}{C}_{13}=-16,20,32$

$C_{\mathrm{ij}}={(-1)}^{i+j}{M}_{\mathrm{ij}}{M}_{23}=\left(\begin{array}{cc}5& 6\\ 4& 8\end{array}\right|=40-24=16C_{23}=\left(-M_{23}\right)=-16M_{13}=\left(\begin{array}{cc}5& 2\\ 4& 8\end{array}\right|=40-8=32C_{13}=\left(M_{13}\right)=32M_{32}=\left(\begin{array}{cc}5& 7\\ 5& 3\end{array}\right|=15-35=-20C_{32}=-M_{32}=20\mathrm{Here}M\mathrm{and}C\mathrm{represents}\mathrm{Minor}\mathrm{and}\mathrm{Cofactor}\mathrm{respectively}.$

option (a) is correct.