Perform matrix addition, subtraction and multiplication by a scalar.

A sports equipment retailer tracks weekly sales quantities for three product categories across two store locations. The table shows the number of units sold in Week 1 and Week 2. Define matrices \(W_1\) and \(W_2\) to represent the sales data for Week 1 and Week 2 respectively, where rows represent locations (North, South) and columns represent categories (Footwear, Apparel, Accessories). (a) Calculate \(W_1 + W_2\) and interpret its meaning in this context. [2 marks] (b) The retailer plans to offer a promotional discount in Week 3. Sales are projected to be 1.5 times the Week 2 sales. Calculate the matrix representing projected Week 3 sales. [2 marks]

Calculate $2\begin{pmatrix} 3 & -1 \\ 4 & 2 \end{pmatrix} - \begin{pmatrix} 2 & 6 \\ 0 & -4 \end{pmatrix}$.

Given matrices \( P = \begin{pmatrix} 4 & -3 \\ 2 & 5 \end{pmatrix} \) and \( Q = \begin{pmatrix} 1 & 6 \\ -2 & 3 \end{pmatrix} \), calculate \( 3P - 2Q \).