tinfoQ

2020-10-27

For each of the pairs of matrices that follow, determine whether it is possible to multiply the first matrix times the second. If it is possible, perform the multiplication.
$\left[\begin{array}{ccc}1& 4& 3\\ 0& 1& 4\\ 0& 0& 2\end{array}\right]\left[\begin{array}{cc}3& 2\\ 1& 1\\ 4& 5\end{array}\right]$

smallq9

Given,
$\left[\begin{array}{ccc}1& 4& 3\\ 0& 1& 4\\ 0& 0& 2\end{array}\right]\left[\begin{array}{cc}3& 2\\ 1& 1\\ 4& 5\end{array}\right]$
Here the order of first matrix is ($3×3$) and the order of second matrix is ($3×2$), therefore the number of columns of first matrix(3) is equal to number of rows of second matrix(3).
Hence multiplication of these matrices is possible.
Therefore,
$\left[\begin{array}{ccc}1& 4& 3\\ 0& 1& 4\\ 0& 0& 2\end{array}\right]\left[\begin{array}{cc}3& 2\\ 1& 1\\ 4& 5\end{array}\right]=\left[\begin{array}{cc}1\left(3\right)+4\left(1\right)+3\left(4\right)& 1\left(2\right)+4\left(1\right)+3\left(5\right)\\ 0\left(3\right)+1\left(1\right)+4\left(4\right)& 0\left(2\right)+1\left(1\right)+4\left(5\right)\\ 0\left(3\right)+0\left(1\right)+2\left(4\right)& 0\left(2\right)+0\left(1\right)+2\left(5\right)\end{array}\right]$
$=\left[\begin{array}{cc}19& 21\\ 17& 21\\ 8& 10\end{array}\right]$

Jeffrey Jordon