Question

If $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$, then find the value of $2A-3B$.

Answer 1

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

$\Rightarrow$ $2A-3B=2\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right]-3\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$

$=\left[\begin{array}{cc}2\times 2& 4\times 2\\ 3\times 2& 2\times 2\end{array}\right]-\left[\begin{array}{cc}3\times 1& 3\times 3\\ -2\times 3& 5\times 3\end{array}\right]$

$=\left[\begin{array}{cc}4& 8\\ 6& 4\end{array}\right]-\left[\begin{array}{cc}3& 9\\ -6& 15\end{array}\right]$

$=\left[\begin{array}{cc}4-3& 8-9\\ 6+6& 4-15\end{array}\right]$

$=\left[\begin{array}{cc}1& -1\\ 12& -11\end{array}\right]$