A recycling table as a matrix
A recycling table as a matrix
Secondary 4
9 marks
Three classes took part in a recycling drive. The table shows the masses, in kilograms, of the materials each class collected.
| Paper | Plastic | Cans | |
|---|---|---|---|
| 4A | 12 | 5 | 3 |
| 4B | 9 | 7 | 4 |
| 4C | 15 | 6 | 2 |
- Write down a matrix \(R\) for the table, with the classes as rows and the materials as columns, in the order shown. State its order.[2]
- Explain what the entry in row 3, column 1 of \(R\) represents.[1]
- Find the sum of the entries in row 2 of \(R\) and explain what it represents.[2]
- Find the sum of the entries in column 1 of \(R\) and explain what it represents.[2]
- Mei writes the same information as a matrix with the materials as rows and the classes as columns. State the entry in row 1, column 2 of her matrix and explain what it represents.[2]
Solution:
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Answer:(a) \(R=\begin{pmatrix}12&5&3\\ 9&7&4\\ 15&6&2\end{pmatrix}\), order \(3\times3\) (b) 4C collected 15 kg of paper (c) \(20\): the mass in kg collected by 4B (d) \(36\): the mass of paper in kg collected by the three classes (e) \(9\): 4B collected 9 kg of paper
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