Question

Three shopkeepers Gaurav, Rizwan and Jacob use carry bags made of polythene, handmade paper and newspaper. The number of polythene bags, handmade bags and newspaper bags used by Gaurav, Rizwan and Jacob are (20, 30, 40), (30, 40, 20) and (40, 20, 30) respectively. One polythene bag costs ₹ 1, one handmade bag is for ₹ 5 and one newspaper bag costs ₹ 2. Gaurav, Rizwan and Jacob spend ₹ A, ₹ B and ₹ C respectively on these carry bags.

Using the concepts of matrices and determinants, answer the following questions:

1. Represent the above information in Matrix form.
2. Find the values of ₹ A, ₹ B and ₹ C.

Answer 1

Let P be a matrix represent the number of bags used by each shopkeeper.

P = `[(20, 30, 40),(30, 40, 20),(40, 20, 30)]`

Let C be matrix represent the cost of each bag

C = `[(1),(5),(2)]`

Let A be matrix represent the total expenditure of each shopkeeper.

Now, A = P × C

`[(A),(B),(C)] = [(20, 30, 40),(30, 40, 20),(40, 20, 30)] [(1),(5),(2)]`

⇒ `[(A),(B),(C)] = [(20 xx 1 + 30 xx 5 + 40 xx 2),(30 xx 1 + 40 xx 5 + 20 xx 2),(40 xx 1 + 20 xx 5 + 30 xx 2)]`

⇒ `[(A),(B),(C)] = [(250),(270),(200)]`

A = ₹ 250, B = ₹ 270 and C = ₹ 200