Question

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.

Answer 1

Quantity matrix:

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

Price matrix:

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

The total amount:

⇒ \[QP = \begin{bmatrix} 15 & 3 & 8 \\ 10 & 4 & 12 \\ 5 & 5 & 9 \end{bmatrix} \times \begin{bmatrix} 170 \\ 150 \\ 250 \end{bmatrix}\]

⇒ \[QP = \begin{bmatrix} 15 \times 170 + 3 \times 150 + 8 \times 250 \\ 10 \times 170 + 4 \times 150 + 12 \times 250 \\ 5 \times 170 + 5 \times 150 + 9 \times 250 \end{bmatrix}\]

⇒ \[QP = \begin{bmatrix} 2550 + 450 + 2000 \\ 1700 + 600 + 3000 \\ 850 + 750 + 2250 \end{bmatrix}\]

⇒ \[QP = \begin{bmatrix} 5000 \\ 5300 \\ 3850 \end{bmatrix}.\]

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