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Use matrix multiplication to answer an application question

Question 1 of 8

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Matrices \(A\) and \(B\) describe low-cost items sold at sports-centre kiosks. The columns of \(A\) and the rows of \(B\) use the same item type order

A: Items sold

Rows, in order: Pool kiosk, Court kiosk, Track kiosk

Columns, in order: Water bottles, Fruit cups

\[A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \\ 3 & 4 \end{bmatrix}\]

B: value for one unit of each item type

Rows, in order: Water bottles, Fruit cups

Columns, in order: Sales value

\[B = \begin{bmatrix} \$1.92 \\ \$1.37 \end{bmatrix}\]
(a)3 marks

Find the product matrix. Its rows are Pool kiosk, Court kiosk, Track kiosk; its columns are Sales value

Rows: Pool kiosk, Court kiosk, Track kiosk. Columns: Sales value ($)

\(AB\)
(b)1 mark

Interpret the entry in row 2, column 1 of \(AB\): Court kiosk and Sales value