Matrices — Case-Study Based Question

Case study:
Neeta, Salma and Vivian are neighbours in different flats of the same building. Last Sunday, they went together to a departmental store to buy groceries.

The groceries purchased by them is as shown below.

The prices of the items are as follows :

Pulses : ₹ 170 per kg

Tea : ₹ 150 per packet

Refined oil : ₹ 250 per litre

Using matrix multiplication, find the total amount that Neeta, Salma and Vivian paid.

Answer

Quantity matrix :

Q = $\begin{bmatrix*}[r] 15 & 3 & 8 \\ 10 & 4 & 12 \\ 5 & 5 & 9 \end{bmatrix*}$

Price matrix :

P = $\begin{bmatrix*}[r] 170 \\ 150 \\ 250 \end{bmatrix*}$

The total amount :

$\Rightarrow QP = \begin{bmatrix*}[r] 15 & 3 & 8 \\ 10 & 4 & 12 \\ 5 & 5 & 9 \end{bmatrix*} \times \begin{bmatrix*}[r] 170 \\ 150 \\ 250 \end{bmatrix*} \\[1em] \Rightarrow QP = \begin{bmatrix*}[r] 15 \times 170 + 3 \times 150 + 8 \times 250 \\ 10 \times 170 + 4 \times 150 + 12 \times 250 \\ 5 \times 170 + 5 \times 150 + 9 \times 250 \end{bmatrix*} \\[1em] \Rightarrow QP = \begin{bmatrix*}[r] 2550 + 450 + 2000 \\ 1700 + 600 + 3000 \\ 850 + 750 + 2250 \end{bmatrix*} \\[1em] \Rightarrow QP = \begin{bmatrix*}[r] 5000 \\ 5300 \\ 3850 \end{bmatrix*}.$

Hence, the total amounts paid by Neeta, Salma and Vivian are ₹ 5,000, ₹ 5,300 and ₹ 3,850.