Question

Using matrices, find the fund collected by school $X$ by selling the above articles.

Answer 1

Taking the transpose of the data

Article/School	Fans	Mats	Toys
School X	30	12	70
School Y	40	15	55
School Z	35	20	75

Let the money collected by respective schools be $X,Y,Z$
Cost per item matrix is $\left[\begin{array}{c}25\\ 100\\ 50\end{array}\right]$

$\left[\begin{array}{ccc}30& 12& 70\\ 40& 15& 55\\ 35& 20& 75\end{array}\right]\left[\begin{array}{c}25\\ 100\\ 50\end{array}\right]=\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]$

Multiplying the matrix

$\left[\begin{array}{c}30\times 25+12\times 100+70\times 50\\ 40\times 25+15\times 100+55\times 50\\ 35\times 25+20\times 100+75\times 50\end{array}\right]=\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]=\left[\begin{array}{c}5450\\ 5250\\ 6665\end{array}\right]$

So, the money collected by School $X$ is $5450$.