Question

If $A=\left[\begin{array}{cc}2& -1\\ 3& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 4\\ 7& 2\end{array}\right]$, then the value $3A-2B$ is

• A. $\left[\begin{array}{cc}3& -11\\ -4& -1\end{array}\right]$
• B. $\left[\begin{array}{cc}4& -1\\ -5& -1\end{array}\right]$
• C. $\left[\begin{array}{cc}4& -11\\ -5& -1\end{array}\right]$
• D. $\left[\begin{array}{cc}4& -11\\ -3& -1\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}4& -11\\ -5& -1\end{array}\right]$

$3A-2B=3\left[\begin{array}{cc}2& -1\\ 3& 1\end{array}\right]-2\left[\begin{array}{cc}1& 4\\ 7& 2\end{array}\right]$

$=\left[\begin{array}{cc}6& -3\\ 9& 3\end{array}\right]-\left[\begin{array}{cc}2& 8\\ 14& 4\end{array}\right]$

$=\left[\begin{array}{cc}6-2& -3-8\\ 9-14& 3-4\end{array}\right]$

$=\left[\begin{array}{cc}4& -11\\ -5& -1\end{array}\right]$