SOLVING SYSTEMS OF EQUATIONS USING INVERSE MATRICES

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

Problem 1 :

2x + 5y = -2 and x + 2y = -3

Solution

Problem 2 :

2x - y = 8, 3x + 2y = -2

Solution

Problem 3 :

2x + 3y - z = 9; x + y + z = 9 and 3x - y - z = -1

Solution

Problem 4 :

x + y + z - 2 = 0, 6x - 4y + 5z - 31 = 0, 5x + 2y + 2z = 13

Solution

Problem 5 :

If

find the products AB  and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2y + z = 7, 2x + y + 3z = 2

Solution

Problem 1 :

A man is appointed in a job with a monthly salary of certain amount and a fixed amount of annual increment. If his salary was 19,800 per month at the end of the first month after 3 years of service and 23,400 per month at the end of the first month after 9 years of service, find his starting salary and his annual increment. (Use matrix inversion method to solve the problem.)

Solution

Problem 2 :

Four men and 4 women can finish a piece of work jointly in 3 days while 2 men and 5 women can finish the same work jointly in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using matrix inversion method.

Solution

Problem 3 :

The prices of three commodities A B, and C are  x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C . Person Q purchases 2
units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C . In the process, P Q, and R earn 15,000, 1,000 and 4,000 respectively. Find the prices per unit of A, B and C. (Use matrix inversion method to solve the problem.)

Solution