Question

If $\left[\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right]A=\left[\begin{array}{ccc}-1& -8& -10\\ 1& -2& -5\\ 9& 22& 15\end{array}\right]$, then sum of all the elements of matrix $A$ is

• A. $0$
• B. $1$
• C. $2$
• D. $-3$

Answer 1

The correct option is B $1$

$\left[\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right]A=\left[\begin{array}{ccc}-1& -8& -10\\ 1& -2& -5\\ 9& 22& 15\end{array}\right]$
let $A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}2& -1\\ 1& 0\\ -3& 4\end{array}\right]\left[\begin{array}{ccc}a& b& c\\ d& e& f\end{array}\right]=\left[\begin{array}{ccc}-1& -8& -10\\ 1& -2& -5\\ 9& 22& 15\end{array}\right]$
$\Rightarrow \left[\begin{array}{ccc}2a-d& 2b-e& 2c-f\\ a& b& c\\ -3a+4d& -3b+4e& -3c+4f\end{array}\right]=\left[\begin{array}{ccc}-1& -8& -10\\ 1& -2& -5\\ 9& 22& 15\end{array}\right]$
$\Rightarrow 2a-d=-1,2b-e=-8,2c-f=-10$ -----(1)
and $a=1,b=-2,c=-5$ ----(2)
from (1) and (2)
$a+b+c=-6$ and $d+e+f=7$
$\therefore$ Sum of all the elements in the matrix $a+b+c+d+e+f=1$
Hence, option B.