Question
Given $A=\left[\begin{array}{ll}1 & 4 \\ 2 & 3\end{array}\right]$ and $B=\left[\begin{array}{ll}-4 & -1 \\ -3 & -2\end{array}\right]$ find a matrix $C$ such that $C+B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
✓
Answer
$\begin{aligned} & A=\left[\begin{array}{ll}1 & 4 \\ 2 & 3\end{array}\right] \\ & B=\left[\begin{array}{ll}-4 & -1 \\ -3 & -2\end{array}\right] \\ & C+B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right] \\ & C=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]-B=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]-\left[\begin{array}{ll}-4 & -1 \\ -3 & -2\end{array}\right] \\ & =\left[\begin{array}{ll}0-(-4) & 0-(-1) \\ 0-(-3) & 0-(-2)\end{array}\right] \\ & =\left[\begin{array}{ll}4 & 1 \\ 3 & 2\end{array}\right] .\end{aligned}$
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