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Combine scalar multiples of matrices

Question 1 of 8

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\(D\) and \(N\) are matrices: \(D\) records the number of pieces of fruit packed into one standard crate at an orchard, while \(N\) records the number packed into one premium crate

In both matrices, the rows are Apples, Pears (top to bottom) and the columns are Tray packs, Loose packs (left to right)

\[D = \begin{bmatrix} 4 & 6 \\ 2 & 5 \end{bmatrix}\]
\[N = \begin{bmatrix} 4 & 4 \\ 5 & 6 \end{bmatrix}\]

An order asks for 5 standard crates and 3 premium crates

4 marks

Work out the matrix \(5D + 3N\), which shows the total number of pieces of fruit of each type in each pack style in the order

\(5D + 3N\)