Question

Find the product of the matrices, if exists.

$\left(\begin{array}{c}6\\ -3\end{array}\right)\left(\begin{array}{cc}2& 7\end{array}\right)$

Answer 1

Product of matrices

${\left(\begin{array}{c}6\\ -3\end{array}\right)}_{2\times 1}{\left(\begin{array}{cc}2& 7\end{array}\right)}_{1\times 2}$

Here the column size of first matrix and row size of the second matrix is same

So multiplication is possible.

The multiplied matrix has the dimension $2\times 2$

${\left(\begin{array}{c}6\\ -3\end{array}\right)}_{2\times 1}{\left(\begin{array}{cc}2& 7\end{array}\right)}_{1\times 2}$

$={\left(\begin{array}{cc}6\times 2& 6\times 7\\ -3\times 2& -3\times 7\end{array}\right)}_{2\times 2}$

$={\left(\begin{array}{cc}12& 42\\ -6& -21\end{array}\right)}_{2\times 2}$