Question

Matrix $A = \begin{bmatrix}1&2&3\\ 1&1&5\\ 2&4&7\end{bmatrix}$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,
$A = \begin{bmatrix}1&2&3\\ 1&1&5\\ 2&4&7\end{bmatrix}$
$ a_{31} =2, a_{32} = 4, a_{33} = 7 $and
$A_{31}=\begin{vmatrix}2&3\\ 1&5\end{vmatrix} $
$= 10 - 3 = 7 $
$A_{32} = -\begin{vmatrix}1&3\\ 1&5\end{vmatrix} $
$= -\left(5 - 3\right) = -2 $
$A_{33} =\begin{vmatrix}1&2\\ 1&1\end{vmatrix} $
$= 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$