Matrices - Application of Matrices
Matrices - Application of Matrices
Secondary 4
Four shops sell different brands of running shoes: Mizuho, Azizs, New Ballast and Nikuu. The table below shows the number of shoes sold by the four shops in a particular week.
| Shop | Mizuho | Azizs | New Ballast | Nikuu |
|---|---|---|---|---|
| Running Sports | \(10\) | \(12\) | \(15\) | \(8\) |
| Real Runners | \(5\) | \(11\) | \(8\) | \(17\) |
| Run Fast | \(16\) | \(4\) | \(7\) | \(6\) |
| Strong Runners | \(6\) | \(8\) | \(4\) | \(11\) |
- Represent the information given in the table above by a \(4 \times 4\) matrix \(S\).
- Mizuho shoes are sold at \(\$160\) each, Azizs shoes at \(\$120\) each, New Ballast shoes at \(\$120\) each and Nikuu shoes at \(\$140\) each. Write down a \(4 \times 1\) matrix \(P\) to represent the selling prices, in dollars, of the different brands of shoes.
- Find \(SP\).
- Explain what the elements in the matrix \(SP\) represent.
- It is given that \(T = \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix}\). Evaluate \(ST\) and explain what the elements of \(ST\) represent.
Solution:
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Answer:(a) \(\begin{pmatrix}10&12&15&8\\5&11&8&17\\16&4&7&6\\6&8&4&11\end{pmatrix}\); (b) \(\begin{pmatrix}160\\120\\120\\140\end{pmatrix}\); (c)(i) \(\begin{pmatrix}5960\\5460\\4720\\3940\end{pmatrix}\); (ii) weekly shop revenues in dollars; (iii) \(\begin{pmatrix}45\\41\\33\\29\end{pmatrix}\), weekly numbers of shoes sold per shop.
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