Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 25– 30, find the product.

Step-by-Step Solution

Answer

The product of the matrices $\left[\begin{array}{cc}4& 1\\ 2& 1\end{array}\right]\left[\begin{array}{cccc}-6& 6& 1& 0\\ 2& 5& 4& -1\end{array}\right]$ is $\left[\begin{array}{cccc}-22& 29& 8& -1\\ -10& 17& 6& -1\end{array}\right]$

Step 1. Given Information

The matrices:

$\left[\begin{array}{cc}4& 1\\ 2& 1\end{array}\right]\left[\begin{array}{cccc}-6& 6& 1& 0\\ 2& 5& 4& -1\end{array}\right]$

Step 2. Observe the matrix

The first matrix is $2\times 2$ matrix and the second matrix is $2\times 4$, so the resultant matrix will be of the form $2\times 4$

Step 3. Find the product

$$\begin{gathered} \left[\begin{array}{cc}4& 1\\ 2& 1\end{array}\right]\left[\begin{array}{cccc}-6& 6& 1& 0\\ 2& 5& 4& -1\end{array}\right]=\left[\begin{array}{cccc}4(-6)+1\left(2\right)& 4\left(6\right)+1\left(5\right)& 4\left(1\right)+1\left(4\right)& 4\left(0\right)+1(-1)\\ 2(-6)+1\left(2\right)& 2\left(6\right)+1\left(5\right)& 2\left(1\right)+1\left(4\right)& 2\left(0\right)+1(-1)\end{array}\right] \\ =\left[\begin{array}{cccc}-22& 29& 8& -1\\ -10& 17& 6& -1\end{array}\right] \end{gathered}$$