Question

11. An electronic company records each type of entertainment device sold at three of their
branch stores so that they can monitor their purchases of supplies. The sales in two
weeks are shown in the following spreadsheets.
Find the sum of the items sold out in two weeks using matrix addition

Answer 1

First of all we should write matrices of all given data 's .
Here, $\mathbf{X}=\left[\begin{array}{cccc}30&15&12&10\\40&20&15&15\\25&18&10&12\end{array}\right]$
Here, X represents items in first of all stores .
rows R₁ represents T.V items
R₂ represents D.V.D items
R₃ represents Videogames items
R₄ represents C.D players items
And columns C₁ represents store 1
C₂ represents store 2
C₃ represents store 3

Similarly $\mathbf{Y}=\left[\begin{array}{cccc}25&12&8&6\\32&10&10&12\\22&15&8&10\end{array}\right]$
Here, Y represents items in 2nd week of all stores .

Now, sum of X and Y
Z = X + Y = $\left[\begin{array}{cccc}30&15&12&10\\40&20&15&15\\25&18&10&12\end{array}\right]+\left[\begin{array}{cccc}25&12&8&6\\32&10&10&12\\22&15&8&10\end{array}\right]$
=$\left[\begin{array}{cccc}55&27&20&16\\72&30&35&27\\47&33&18&22\end{array}\right]$
Hence, $\mathbb{Z}=\left[\begin{array}{cccc}55&27&20&16\\72&30&35&27\\47&33&18&22\end{array}\right]$ represents required matrix