Question

If $A=\left[\begin{array}{ccc}-1& 0& 2\\ 3& 1& 4\end{array}\right],B=\left[\begin{array}{ccc}0& -2& 5\\ 1& -3& 1\end{array}\right]$ and $C=\left[\begin{array}{ccc}1& -5& -2\\ 6& 0& -4\end{array}\right],$ then $2A-3B+4C$ is

• A. $\left[\begin{array}{ccc}2& -14& -19\\ 27& 11& -11\end{array}\right]$
• B. $\left[\begin{array}{ccc}2& 11& -19\\ -14& 11& -11\end{array}\right]$
• C. $\left[\begin{array}{ccc}2& -14& -19\\ 11& 17& -11\end{array}\right]$
• D. $\left[\begin{array}{ccc}-14& -14& -2\\ 17& 11& -11\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{ccc}2& -14& -19\\ 27& 11& -11\end{array}\right]$

$2A=2\left[\begin{array}{ccc}-1& 0& 2\\ 3& 1& 4\end{array}\right]=\left[\begin{array}{ccc}-2& 0& 4\\ 6& 2& 8\end{array}\right]$

$3B=3\left[\begin{array}{ccc}0& -2& 5\\ 1& -3& 1\end{array}\right]=\left[\begin{array}{ccc}0& -6& 15\\ 3& -9& 3\end{array}\right]$

$4C=4\left[\begin{array}{ccc}1& -5& -2\\ 6& 0& -4\end{array}\right]=\left[\begin{array}{ccc}4& -20& -8\\ 24& 0& -16\end{array}\right]$

$2B-3B+4C=\left[\begin{array}{ccc}-2& 0& 4\\ 6& 2& 8\end{array}\right]-\left[\begin{array}{ccc}0& -6& 15\\ 3& -9& 3\end{array}\right]+\left[\begin{array}{ccc}4& -20& -8\\ 24& 0& -16\end{array}\right]$

$=\left[\begin{array}{ccc}-2-0+4& 0+6-20& 4-15-8\\ 6-3+24& 2+9+0& 8-3-16\end{array}\right]$

$=\left[\begin{array}{ccc}2& -14& -19\\ 27& 11& -11\end{array}\right]$

Hence, $2A-3B+4C=\left[\begin{array}{ccc}2& -14& -19\\ 27& 11& -11\end{array}\right]$