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.

	Pulses(kg)	Tea packets	Refined oil(litre)
1.Neeta	15	3	8
2.Salma	10	4	12
3.Vivian	5	5	9

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.

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.