Choosing a matrix for totals

Choosing a matrix for totals

Secondary 3
4 marks
TGM Original Questions

A factory packs small and large boxes on three days. The matrix \(Q=\begin{pmatrix}18&12\\ 25&15\\ 20&10\end{pmatrix}\) has rows Monday, Tuesday, Wednesday and columns small, large boxes.

  1. Choose either \(u=\begin{pmatrix}1\\ 1\end{pmatrix}\) or \(v=\begin{pmatrix}1&1&1\end{pmatrix}\) to form a product giving each day's total number of boxes. Write and evaluate the product.[3]
  2. A van carries at most 35 boxes. On which day is more than one trip needed? Give a reason.[1]

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Answer:(a) \(Qu=\begin{pmatrix}30\\ 40\\ 30\end{pmatrix}\) (b) Tuesday; 40 exceeds 35.

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