Chapter 4, Problem 18SGR

To determine

To find: The total amount of money Martin spent at the grocery store by using matrix multiplication.

Answer to Problem 18SGR

The total amount of money Martin spent at the grocery store is $\$28.65$ .

Explanation of Solution

Given:

The given matrix that shows the price of each item is:

  $A={\left[\begin{array}{cccc}\$2.59& \$0.49& \$5.25& \$3.99\end{array}\right]}_{1\times 4}$

Here,

The price of 1 gallon milk is $\$2.59$ .

The price of 1 apple is $\$0.49$ .

The price of 1 frozen dinner is $\$5.25$ .

The price of 1 box of cereal is $\$3.99$ .

In order to find the total amount of money Martin spent at the grocery store by using matrix multiplication, first, represent the number of items bought by Martin in column matrix form.

The column matrix of the number of item bought is given as:

  $B={\left[\begin{array}{c}1\\ 2\\ 4\\ 1\end{array}\right]}_{4\times 1}$

As, the matrix $A$ has the number of columns are $4$ and the matrix $B$ has the number of rows are $4$ ,

So the product of the matrices $A$ and $B$ is possible.

The total amount of money Martin spent at the grocery store by using matrix multiplication is calculated as:

  $\begin{array}{c}AB=\left[\begin{array}{cccc}\$2.59& \$0.49& \$5.25& \$3.99\end{array}\right]\cdot \left[\begin{array}{c}1\\ 2\\ 4\\ 1\end{array}\right]\\ =\left[\$2.59\times 1+\$0.49\times 2+\$5.25\times 4+\$3.99\times 1\right]\\ =\left[\$28.56\right]\end{array}$

Therefore, the total amount of money Martin spent at the grocery store is $\$28.65$ .