Question

If $A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$, then $2A-B$ is

• A. $\left[\begin{array}{ccc}3& 5& 3\\ -5& 6& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}-5& 5& 3\\ 5& 6& 0\end{array}\right]$
• C. $\left[\begin{array}{ccc}-1& 5& 3\\ 5& 6& 0\end{array}\right]$
• D. $\left[\begin{array}{ccc}-1& -1& 3\\ 5& 6& 0\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{ccc}-1& 5& 3\\ 5& 6& 0\end{array}\right]$

We have
$2A-B=2\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\end{array}\right]-\left[\begin{array}{ccc}3& -1& 3\\ -1& 0& 2\end{array}\right]$

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

$=\left[\begin{array}{ccc}2-3& 4+1& 6-3\\ 4+1& 6+0& 2-2\end{array}\right]=\left[\begin{array}{ccc}-1& 5& 3\\ 5& 6& 0\end{array}\right]$