Question

Find the product of the matrices, if exists.
$\left[\begin{array}{ccc}2& 9& -3\\ 4& -1& 0\end{array}\right]\left[\begin{array}{cc}4& 2\\ -6& 7\\ -2& 1\end{array}\right]$

Answer 1

$\left(\begin{array}{ccc}2& 9& -3\\ 4& -1& 0\end{array}\right)\left(\begin{array}{cc}4& 2\\ -6& 7\\ -2& 1\end{array}\right)$

using the multiplication properties of matrices, we get

$\left(\begin{array}{cc}2\times 4+9\times (-6)+(-3)\times (-2)& 2\times 2+9\times 7+(-3)\times 1\\ 4\times 4+(-1)\times (-6)+0\times (-2)& 4\times 2+(-1)\times 7+0\times 1\end{array}\right)$

$=\left(\begin{array}{cc}-40& 64\\ 22& 1\end{array}\right)$