12th Maths Guide Solution Appliaction of matrices and determinants Exercise 1.3
Here are the Class 12th maths solutions of Chapter 1 Application of Matrices and Determinants Exercise 1.3, according to the Samacheer Kalvi syllabus for Tamil Nadu state board students.
Question no 1: Solve the following system of linear equations by the matrix inversion method.
(i) 2x + 5y = -2, x + 2y = -3
Solution:
(ii) 2x – y = 8, 3x + 2y = -2
Solution:
(iii) 2x + 3y – z = 9, x + y + z = 9, 3x – y – z = -1
Solution:
(iv) x + y + z – 2 = 0, 6x – 4y + 5z – 31 = 0, 5x + 2y + 2z = 13
Question No 2:
Question no 3:
A man is appointed to a job with a monthly salary package of a certain amount and a fixed amount of annual increment. If his salary was Rs 19,800 per month, then at the end of the first month after 3 years of service, and Rs 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 the matrix inversion method to solve the problem.
Solution:
Question no 4.:
4 men and 4 women can finish work together in 3 days, while 2 men and 5 women can finish the same work together in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using the matrix inversion method.
Solution:
Let’s consider that the time taken by one man is x days, and one woman is y days.
Question no 5:
The prices of three commodities A, B, & C are Rs x, y, and z per unit, respectively. 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 units of B and one unit of C. In the process, P, Q & R earn Rs 15,000, Rs 1,000 & 14,000 respectively. Find the prices per unit of A, B, and C. Use the matrix inversion method to solve the problem.
Solution:
