Q31. - Algebra 2

Question

For exercises 30-32, use the following information. The Cookie Cutter Bakery records each type of cookie sold at three of their branch stores. Two days of sales are shown in the spreadsheets below.

 

31. Find the sum of the two days’ sales expressed as a matrix.

Step-by-Step Solution

Answer

The sum of the two days’ sales expressed as a matrix is 

$\left[\begin{array}{cccc}332& 184& 130& 149\\ 164& 124& 75& 130\\ 160& 182& 72& 108\end{array}\right]$.

Step 1 - Define concept of matrix addition

If A and B are two matrices of order $m\times n$, then the addition of the two matrices will also yield a matrix of order $m\times n$wherein each element is the sum of the corresponding elements.

Step 2 - Add corresponding elements

The data in the table is organized in two matrices A and B. Add corresponding elements of both the matrices so as to find the sum of two day’s sales.

$\begin{array}{c}A+B=\left[\begin{array}{cccc}120& 97& 64& 75\\ 80& 59& 36& 60\\ 72& 84& 29& 48\end{array}\right]+\left[\begin{array}{cccc}112& 87& 56& 74\\ 84& 65& 39& 70\\ 88& 98& 43& 60\end{array}\right]\\ =\left[\begin{array}{cccc}120+112& 97+87& 64+56& 75+74\\ 80+84& 59+65& 36+39& 60+70\\ 72+88& 84+98& 29+43& 48+60\end{array}\right]\end{array}$

Step 3 - Simplify the matrix

Further simplify the matrix.

$\begin{array}{c}A+B=\left[\begin{array}{cccc}120+112& 97+87& 64+56& 75+74\\ 80+84& 59+65& 36+39& 60+70\\ 72+88& 84+98& 29+43& 48+60\end{array}\right]\\ =\left[\begin{array}{cccc}332& 184& 130& 149\\ 164& 124& 75& 130\\ 160& 182& 72& 108\end{array}\right]\end{array}$