Question
If $3 A-B=\left[\begin{array}{ll}5 & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}4 & 3 \\ 2 & 5\end{array}\right]$, then find the matrix $A.$
✓
Answer
Given $3 A-B=\left[\begin{array}{ll}5 & 0 \\ 1 & 1\end{array}\right], B=\left[\begin{array}{ll}4 & 3 \\ 2 & 5\end{array}\right]$
$\text { or } 3 A-\left[\begin{array}{ll}4 & 3 \\2 & 5\end{array}\right]=\left[\begin{array}{ll}5 & 0 \\1 & 1\end{array}\right]$
$\begin{array}{l}\text { or } 3 A=\left[\begin{array}{ll}5 & 0 \\ 1 & 1\end{array}\right]+\left[\begin{array}{ll}4 & 3 \\ 2 & 5\end{array}\right] \\ \text { or } 3 A=\left[\begin{array}{ll}9 & 3 \\ 3 & 6\end{array}\right] \\ \text { or } A=\left[\begin{array}{ll}3 & 1 \\ 1 & 2\end{array}\right]\end{array}$
$\text { or } 3 A-\left[\begin{array}{ll}4 & 3 \\2 & 5\end{array}\right]=\left[\begin{array}{ll}5 & 0 \\1 & 1\end{array}\right]$
$\begin{array}{l}\text { or } 3 A=\left[\begin{array}{ll}5 & 0 \\ 1 & 1\end{array}\right]+\left[\begin{array}{ll}4 & 3 \\ 2 & 5\end{array}\right] \\ \text { or } 3 A=\left[\begin{array}{ll}9 & 3 \\ 3 & 6\end{array}\right] \\ \text { or } A=\left[\begin{array}{ll}3 & 1 \\ 1 & 2\end{array}\right]\end{array}$
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