Chapter 12, Problem 27MCQ

Solution

To find: The total sales using two matrices.

The total sales is $130.

Given information:

Given,a store sells three kinds of pencils. The first matrix below shows the prices, in dollars, for each type. The second matrix shows the quantity sold for each type.

  

Calculation:

The total sales of the store can be determined using matrix multiplication as in the multiplication, the multiplication goes rows to columns. Hence the cost of each type would be multiplied to corresponding quantity and then they are added to give the total sales.

Multiplying the matrices:

  $\begin{array}{l}\left[\begin{array}{ccc}3& 4& 2\end{array}\right]\cdot \left[\begin{array}{c}20\\ 10\\ 15\end{array}\right]=\left[\left(3\right)\left(20\right)+\left(4\right)\left(10\right)+\left(2\right)\left(15\right)\right]\\ \left[\begin{array}{ccc}3& 4& 2\end{array}\right]\cdot \left[\begin{array}{c}20\\ 10\\ 15\end{array}\right]=\left[60+40+30\right]\\ \left[\begin{array}{ccc}3& 4& 2\end{array}\right]\cdot \left[\begin{array}{c}20\\ 10\\ 15\end{array}\right]=\left[130\right]\end{array}$

Conclusion:

The total sales is $130.