EXERCISE 1.3
1. Solve the following system of linear equations by matrix
inversion method:
(i) 2x +
5 y = -2, x + 2 y = -3
(ii) 2x - y = 8, 3x + 2 y = -2
(iii) 2x + 3y - z = 9, x + y + z = 9, 3x - y - z = -1
(iv) x + y + z - 2 = 0, 6x - 4 y + 5z - 31 = 0, 5x + 2 y + 2z = 13
2. If find the products AB and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2 y + z = 7, 2x + y + 3z = 2.
3. 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.)
4. 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.
5. 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.)
Answers for Exercise 1.3:
1. (i) x = -11, y = 4
(ii) x = 2, y = -4
(iii) x = 2, y = 3, z = 4
(iv) x = 3, y = -2, z = 1
2. x = 2, y = 1, z = -1
3. ₹ 18000, ₹ 600
4. 18 days, 36 days
5. ₹ 2000, ₹ 1000, ₹ 3000
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