Question

If $A=\left[\begin{array}{cc}2& 2\\ -3& 1\\ 4& 0\end{array}\right],B=\left[\begin{array}{cc}6& 2\\ 1& 3\\ 0& 4\end{array}\right]$, find matrix $C$ such that $A+B+C=0$, where $O$ is the zero matrix.

Answer 1

$A=\left[\begin{array}{cc}2& 2\\ -3& 1\\ 4& 0\end{array}\right]B=\left[\begin{array}{cc}6& 2\\ 1& 3\\ 0& 4\end{array}\right]$

$A+B+C=0$

$\left[\begin{array}{cc}6& 2\\ 1& 3\\ 0& 4\end{array}\right]+\left[\begin{array}{cc}2& 2\\ -3& 1\\ 4& 0\end{array}\right]+C=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\end{array}\right]$

$\left[\begin{array}{cc}6+2& 2+2\\ 1-3& 3+1\\ 0+4& 4+0\end{array}\right]+C=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\end{array}\right]$

$\left[\begin{array}{cc}8& 4\\ -2& 4\\ 4& 4\end{array}\right]+C=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 0& 0\end{array}\right]$

$C=\left[\begin{array}{cc}-8& -4\\ 2& -4\\ -4& -4\end{array}\right]$