1. **State the problem:** We are given a table showing the labour hours, wood blocks, and paint tins required to manufacture toy buses and trains, along with their costs. We need to represent this data as matrices and perform matrix operations to find manufacturing costs. 2. **Represent the matrix A:** The matrix A contains the quantities of labour, wood, and paint for each toy. $$A = \begin{bmatrix} 6 & 4 & 3 \\ 3 & 4 & 2 \end{bmatrix}$$ 3. **State the order of matrix A:** Matrix A has 2 rows and 3 columns, so its order is $2 \times 3$. 4. **Find and state the order of $A^T$ (transpose of A):** Transposing swaps rows and columns. $$A^T = \begin{bmatrix} 6 & 3 \\ 4 & 4 \\ 3 & 2 \end{bmatrix}$$ The order of $A^T$ is $3 \times 2$. 5. **Write the cost column matrix C:** Labour costs 8 per hour, wood 1 per block, paint 2 per tin. $$C = \begin{bmatrix} 8 \\ 1 \\ 2 \end{bmatrix}$$ 6. **Calculate the cost of manufacturing one toy bus and one toy train using matrix multiplication:** $$AC = \begin{bmatrix} 6 & 4 & 3 \\ 3 & 4 & 2 \end{bmatrix} \times \begin{bmatrix} 8 \\ 1 \\ 2 \end{bmatrix} = \begin{bmatrix} 6 \times 8 + 4 \times 1 + 3 \times 2 \\ 3 \times 8 + 4 \times 1 + 2 \times 2 \end{bmatrix} = \begin{bmatrix} 48 + 4 + 6 \\ 24 + 4 + 4 \end{bmatrix} = \begin{bmatrix} 58 \\ 32 \end{bmatrix}$$ 7. **Determine which toy is more expensive:** The bus costs 58 to manufacture, the train costs 32. Therefore, the toy bus is more expensive to manufacture because $58 > 32$. **Final answer:** The toy bus costs 58 and the toy train costs 32 to manufacture; the bus is more expensive.