Question

Mr. A went to a market to purchase 3 kg of sugar, 10 kg of wheat and 1 kg of salt. In a shop near to Mr. A’s residence, these commodities are priced at Rs. 20, Rs. 10 and Rs. 8 per kg whereas in the local market these commodities are priced at Rs. 15, Rs. 8 and Rs. 6 per kg respectively. If cost of travelling to local market is Rs. 25, find the net savings of Mr. A using matrix multiplication.​

Answer 1

Step-by-step explanation:

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Answer 2

Concept

To do multiplication of two matrices, the number of columns in the first matrix must be equal to number of rows in second matrix and the resultant matrix will have the number of rows of the 1 matrix and no of columns of the second matrix.

Given

3kg sugar, 10kg wheat, 1kg salt

Shop 1  Rs. 20, Rs. 10, Rs. 8 per kg

Shop 2 Rs. 15, Rs. 8, Rs. 6 per kg

Find

Net savings of Mr A

Solution

Let C1 be the prices of the shop near to his house and C2 be the prices of the shop at local market.

C1 =  $\left[\begin{array}{c}20&10&18\end{array}\right]$

C2 = $\left[\begin{array}{c}15&8&6\end{array}\right]$  

Let Q denotes the amount needed for Mr A

Q =  $\left[\begin{array}{c}3&10&1\end{array}\right]$

Total price he pays equals to (Q' Ci)

Thus the diffrence between prices in two shops is

Q'C1 - Q'C2 = Q'(C1 - C2)

Q'(C1 - C2) =  $\left[\begin{array}{ccc}3&10&1\end{array}\right]$ $\left[\begin{array}{c}20&10&18\end{array}\right]$ - $\left[\begin{array}{ccc}3&10&1\end{array}\right]$ $\left[\begin{array}{c}15&8&6\end{array}\right]$

Q'(C1 - C2) = 15 + 20 + 2 = 37

Since travelling to local market costs Rs. 25

Net savings = 37-25 = 12

Net savings of Mr A is Rs. 12

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