Matrices - Application of Matrices
Matrices - Application of Matrices
Secondary 4
The number of Chinese and English copies of a textbook that were sold in three outlets of a bookstore in a particular month are shown in the following table.
| Chinese | English | |
|---|---|---|
| Tampines | \(35\) | \(46\) |
| Bishan | \(43\) | \(70\) |
| Jurong | \(38\) | \(58\) |
The average printing cost of a Chinese and an English textbook is \(\$15\) and \(\$10\) respectively. The information in the above table can be represented by the following matrices \(N = \begin{pmatrix} 35 & 46 \\ 43 & 70 \\ 38 & 58 \end{pmatrix} \text{ and}\hspace{0.5em} C = \begin{pmatrix} 15 \\ 10 \end{pmatrix}.\)
- Evaluate \(NC\).
- State what the elements of \(NC\) represent.
- The corresponding selling price of the textbooks can be represented by the matrix \(S = \begin{pmatrix} 27 \\ 18 \end{pmatrix}\).
- Evaluate matrix \(B = N(S - C)\).
- State what the elements of \(B\) represent.
- Evaluate the matrix \(R = \frac{1}{3}(1 \quad 1 \quad 1)B\).
- State what \(R\) represents.
Solution:
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Answer:(a)(i) \(\begin{pmatrix}985\\1345\\1150\end{pmatrix}\); (ii) printing costs of books sold at each outlet. (b)(i) \(\begin{pmatrix}788\\1076\\920\end{pmatrix}\); (ii) revenues less printing costs per outlet. (c)(i) \(\begin{pmatrix}928\end{pmatrix}\); (ii) average monthly profit per outlet in dollars, on the stated cost basis.
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