Question:
If $A=\left[\begin{array}{cc}-2 & 3 \\ 4 & 5 \\ 1 & -6\end{array}\right]$ and $B=\left[\begin{array}{cc}5 & 2 \\ -7 & 3 \\ 6 & 4\end{array}\right]$, find a matrix $C$ such that $A+B-C=0$
Solution:
Given A + B – C = 0
$\left[\begin{array}{cc}-2 & 3 \\ 4 & 5 \\ 1 & -6\end{array}\right]+\left[\begin{array}{cc}5 & 2 \\ -7 & 3 \\ 6 & 4\end{array}\right]-C=0$
$\begin{aligned} C &=\left[\begin{array}{cc}-2 & 3 \\ 4 & 5 \\ 1 & -6\end{array}\right]+\left[\begin{array}{cc}5 & 2 \\ -7 & 3 \\ 6 & 4\end{array}\right] \\ C &=\left[\begin{array}{cc}3 & 5 \\ -3 & 8 \\ 7 & -2\end{array}\right] \end{aligned}$
Conclusion: $C=\left[\begin{array}{cc}3 & 5 \\ -3 & 8 \\ 7 & -2\end{array}\right]$