Question

Compute

$\left[\begin{array}{ccc}-1& 3& 0\\ 2& 1& 4\end{array}\right]\times \left[\begin{array}{cc}1& 3\\ 0& 2\\ -2& -1\end{array}\right]$

• A. $\left[\begin{array}{cc}1& 3\\ 6& -4\end{array}\right]$
• B. $\left[\begin{array}{cc}-1& -3\\ 6& 4\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& 3\\ -6& 4\end{array}\right]$
• D. $\left[\begin{array}{cc}-1& 3\\ -6& -4\end{array}\right]$

Answer 1

The correct option is C

$\left[\begin{array}{cc}-1& 3\\ -6& 4\end{array}\right]$

Use matrix multiplication to simplify the expression:

Given: $\left[\begin{array}{ccc}-1& 3& 0\\ 2& 1& 4\end{array}\right]\times \left[\begin{array}{cc}1& 3\\ 0& 2\\ -2& -1\end{array}\right]$

Multiply the rows of the first matrix to the column of the second matrix to get the product matrix.

$\begin{array}{rcl}\left[\begin{array}{ccc}-1& 3& 0\\ 2& 1& 4\end{array}\right]\times \left[\begin{array}{cc}1& 3\\ 0& 2\\ -2& -1\end{array}\right]& =& \left[\begin{array}{cc}-1·1+3·0+0·(-2)& -1·3+3·2+0·(-1)\\ 2·1+1·0+4·(-2)& 2·3+1·2+4·(-1)\end{array}\right]\\ & =& \left[\begin{array}{cc}-1& 3\\ -6& 4\end{array}\right]\end{array}$

Hence, option (C) is the correct answer.