Combine scalar multiples of matrices
The matrix \(P\) below records the weekly order list of a hardware chain's city depot. The matrix \(N\) records the weekly order list of its coastal depot
In both matrices, the rows are Paint tins, Brush sets (top to bottom) and the columns are Interior, Exterior (left to right)
\[P = \begin{bmatrix} 1 & 3 \\ 6 & 5 \end{bmatrix}\]
\[N = \begin{bmatrix} 3 & 1 \\ 6 & 3 \end{bmatrix}\]
Head office weights the two depots differently in its combined order: it orders 2 times the city depot's list and 3 times the coastal depot's list