Solve the following system of linear equations by matrix inversion method :

x + 2y + 3z = 6

2x + 4y + z = 7

3x + 2y + 9z = 14

The sales (in Rs. ‘000) of a product of a company in two districts A and B are shown in the following table. Find the coefficient of variation of the sales and determine which district is consistent in sales.

Sales 10-12 13-15 16-18 17-19 19-21 21-23 23-25

A 24 50 90 60 30 15 7

B 15 59 85 70 25 10 8

(a) The cost of fuel for running a train is proportional to the square of the speed it generates in Km. per hour. It costs Rs. 750 per hour, at a speed of 60 km, per hour. Find the most economical speed if the fixed charges are Rs. 1,000 per hour.

x + 2y + 3z = 6

2x + 4y + z = 7

3x + 2y + 9z = 14

The sales (in Rs. ‘000) of a product of a company in two districts A and B are shown in the following table. Find the coefficient of variation of the sales and determine which district is consistent in sales.

Sales 10-12 13-15 16-18 17-19 19-21 21-23 23-25

A 24 50 90 60 30 15 7

B 15 59 85 70 25 10 8

(a) The cost of fuel for running a train is proportional to the square of the speed it generates in Km. per hour. It costs Rs. 750 per hour, at a speed of 60 km, per hour. Find the most economical speed if the fixed charges are Rs. 1,000 per hour.