Question

$1fA=\left[\begin{array}{ccc}1& 5& -6\\ -8& 0& 4\\ 3& -7& 2\end{array}\right]$ then the cofactors of the elements $3,-7,2$ are p,q,r respectively their ascending order is

• A. $p,r,q$
• B. $q,r,p$
• C. $p,q,r$
• D. $r,p,q$

Answer 1

Answer: (A)

$p,r,q$

$A=\left[\begin{array}{ccc}1& 5& -6\\ -8& 0& 4\\ 3& -7& 2\end{array}\right]$

Cofactor of $3=c_{31}=\left|\begin{array}{cc}5& -6\\ 0& 4\end{array}\right|=5\times 4-0(-6)=20=p$

Cofactor of $-7=c_{32}=-\left|\begin{array}{cc}1& -6\\ -8& 4\end{array}\right|=-(1\times 4-(-8)(-6))=-(4-48)=44=q$

Cofactor of $2=c_{33}=\left|\begin{array}{cc}1& 5\\ -8& 0\end{array}\right|=1\times 0-(-8)\left(5\right)=40=r$

$\therefore$ In ascending order $p,r,q$