Chapter 11.4, Problem 29AYU

To determine

To calculate: The product of the matrices $\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$ .

Answer to Problem 29AYU

The product of the matrices $\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$ is $\left[\begin{array}{cc}9& 2\\ 34& 13\\ 47& 20\end{array}\right]$ .

Explanation of Solution

Given information:

The matrices a $\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$ .

Formula used:

To find the product AB of two matrices A and B, the number of column in matrix A must be equal to number of rows in matrix B.

Calculation:

Consider the matrices are $\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$

Recall that to find the product AB of two matrices A and B, the number of column in matrix A must be equal to number of rows in matrix B.

  $\begin{array}{c}\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]=\left[\begin{array}{cc}1+0+8& 3+0-1\\ 2+24+8& 6+8-1\\ 3+36+8& 9+12-1\end{array}\right]\\ =\left[\begin{array}{cc}9& 2\\ 34& 13\\ 47& 20\end{array}\right]\end{array}$

Thus, the product of the matrices $\left[\begin{array}{ccc}1& 0& 1\\ 2& 4& 1\\ 3& 6& 1\end{array}\right]\left[\begin{array}{cc}1& 3\\ 6& 2\\ 8& -1\end{array}\right]$ is $\left[\begin{array}{cc}9& 2\\ 34& 13\\ 47& 20\end{array}\right]$ .