Q. 29 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 25– 30, find the product.

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

Step-by-Step Solution

Answer

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 $\left[\begin{array}{cc}9& 2\\ 34& 13\\ 47& 20\end{array}\right]$

Step 1. Given Information

The matrices:

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

Step 2. Observe the matrix

The first matrix is $3\times 3$ matrix and the second matrix is $3\times 2$, so the resultant matrix will be of the form $3\times 2$ matrix

Step 3. Find the product

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