Three shopkeepers, A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40 paise, a pen costs Rs 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill.

Matching exercise

Match the items on the right to the items on the left.

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

STEP 6

A: 12 dozen notebooks, 5 dozen pens and 6 dozen pencils B: 10 dozen notebooks, 6 dozen pens and 7 dozen pencils C: 11 dozen notebooks, 13 dozen pens and 8 dozen pencils

Matrix representaion of A,B,C

Hence, the cost of purchasing one dozen of the items can be represented in matrix form with each row corresponding to an item as –

Now, the individual bill for each shopkeeper can be found by taking the product of the matrices X and Y.

Thus, the bills of shopkeepers A, B and C are Rs 157.80, Rs 167.40 and Rs 281.40 respectively.