NIMCET 2017 — Mathematics PYQ

Concept:
Two matrices may be added or subtracted only if they have the same dimension; that is, they must have the samenumber of rows and columns.
Addition or subtraction is accomplished by adding or subtracting corresponding elements.

Calculation

Given,  
$A=\left[\begin{array}{cc}-1& amp;2\\ 3& amp;4\end{array}\right]$  
and 
$B=\left[\begin{array}{cc}3& amp;-2\\ 1& amp;5\end{array}\right]$  

Consider, $2A+B+X=0$  

$\Rightarrow 2\left[\begin{array}{cc}-1& amp;2\\ 3& amp;4\end{array}\right]+\left[\begin{array}{cc}3& amp;-2\\ 1& amp;5\end{array}\right]+X=\left[\begin{array}{cc}0& amp;0\\ 0& amp;0\end{array}\right]$  

$\Rightarrow \left[\begin{array}{cc}1& amp;2\\ 7& amp;13\end{array}\right]+X=\left[\begin{array}{cc}0& amp;0\\ 0& amp;0\end{array}\right]$  

$\Rightarrow X=\left[\begin{array}{cc}0& amp;0\\ 0& amp;0\end{array}\right]-\left[\begin{array}{cc}1& amp;2\\ 7& amp;13\end{array}\right]$  

$\Rightarrow X=\left[\begin{array}{cc}-1& amp;-2\\ -7& amp;-13\end{array}\right]$