Mathematical Modeling with Matrices
Mathematical Modeling with Matrices
Secondary 4
The table below records the number of \(\$2\), \(\$5\) and \(\$10\) notes \(3\) children, Alvin, Brian and Colin has.
| \(\$2\) | \(\$5\) | \(\$10\) | |
|---|---|---|---|
| Alvin | \(3\) | \(1\) | \(1\) |
| Brian | \(1\) | \(3\) | \(0\) |
| Colin | \(0\) | \(2\) | \(3\) |
The information in the table can be represented by a matrix \(P\).
- Write down the matrix \(P\).
- Calculate \(PS\) where \(S = \begin{pmatrix} 2 \\ 5 \\ 10 \end{pmatrix}\).
- Describe what is represented by the elements of \(PS\).
- Given that \(Q = \begin{pmatrix} 1 & 1 & 1 \end{pmatrix}\), calculate \(R = QP\).
- Describe what is represented by the elements of \(R\).
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Answer:(a) \(\begin{pmatrix}3&1&1\\1&3&0\\0&2&3\end{pmatrix}\); (b) \(\begin{pmatrix}21\\17\\40\end{pmatrix}\); (c) total dollars held by Alvin, Brian and Colin; (d) \(\begin{pmatrix}4&6&4\end{pmatrix}\); (e) combined counts of the SGD 2, SGD 5 and SGD 10 notes.
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