Chapter 12, Problem 15GR

Solution

To find: The total number of items sold using the matrix addition.

Given information:

Suppose you have twelve tables, one for each month of the museum’s sales in the previous problem. These can be combined using the matrix addition to determine the total number of items sold in each category during the year. Describe how this is done. Use several examples like the one you made in previous problem to see if this method works.

Explanation:

Let the three stores $A,B,$ and $C$

sold the following number of tables, chairs and lamps during a month:

Items	A	B	C
Tables	15	9	7
Chairs	6	5	4
Lamps	7	2	3

Use matrix addition to find the total number of tables, chairs and lamps sold from the three stores during a month.

Enter the given information in matrices as follows:

  $\begin{array}{l}A=\left[\begin{array}{c}15\\ 6\\ 7\end{array}\right],B=\left[\begin{array}{c}9\\ 5\\ 2\end{array}\right],C=\left[\begin{array}{c}7\\ 4\\ 3\end{array}\right]\\ A+B+C=\left[\begin{array}{c}15+9+7\\ 6+5+4\\ 7+2+3\end{array}\right]=\left[\begin{array}{c}31\\ 15\\ 12\end{array}\right]\end{array}$

Hence, $31$ tables, $15$ chairs and $12$ lamps were sold from the three stores during a month.