Question

Matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 5\\ 2& 4& 7\end{array}\right]$then the value of $a_{31}{A}_{31}+a_{32}{A}_{32}+a_{33}+A_{33}$ is

• A. 1
• B. 13
• C. -1
• D. -13

Answer 1

Answer: (C)

We have,
$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 5\\ 2& 4& 7\end{array}\right]$
$a_{31}=2,a_{32}=4,a_{33}=7$and
$A_{31}=\left|\begin{array}{cc}2& 3\\ 1& 5\end{array}\right|$
$=10-3=7$
$A_{32}=-\left|\begin{array}{cc}1& 3\\ 1& 5\end{array}\right|$
$=-\left(5-3\right)=-2$
$A_{33}=\left|\begin{array}{cc}1& 2\\ 1& 1\end{array}\right|$
$=1-2=-1$
$\therefore a_{31}{A}_{31}+a_{32}{A}_{32}+a_{33}{A}_{33}$
$=2(7)+4(-2)+7(-1)$
$=14-8-7=-1$