Matrices - Application of Matrices

A rice distributor supplies rice to \(4\) different supermarkets in Singapore. The number of bags of rice supplied per delivery to each supermarket, the sizes and cost price are shown in the table below.

1. 1. If \(\mathbf{P} = \begin{pmatrix} 40 & 25 & 10 \end{pmatrix}\), evaluate \(6\mathbf{P}\).
   2. Describe what is represented by the elements of \(6\mathbf{P}\).
2. 1. If \(\mathbf{Q} = \begin{pmatrix} 40 & 25 & 10 \\ 80 & 60 & 30 \\ 30 & 20 & 25 \\ 40 & 35 & 30 \end{pmatrix}\) and \(\mathbf{R} = \begin{pmatrix} 4 \\ 7 \\ 12 \end{pmatrix}\), evaluate \(\mathbf{QR}\).
   2. Describe what is represented by the elements of \(\mathbf{QR}\).
3. 1. Write down two matrices such that the product under the matrix multiplication give the total number of each size of bag the distributor supply to the four supermarkets in one month.
   2. Evaluate the product of the two matrices in (c)(i).
4. Using the product from part (c)(ii) and multiplying by another matrix, evaluate the total amount of money the distributor received from the four supermarkets in one month.