Exercise 1.6: Matrix: Non-homogeneous Linear Equations

EXERCISE 1.6

1. Test for consistency and if possible, solve the following systems of equations by rank method.

(i) x - y + 2z = 2, 2x + y + 4z = 7, 4x - y + z = 4 

(ii) 3x + y + z = 2, x - 3y + 2z = 1, 7x - y + 4z = 5 

(iii) 2x + 2 y + z = 5, x - y + z = 1, 3x + y + 2z = 4

(iv) 2x - y + z = 2, 6x - 3y + 3z = 6,  4x - 2y + 2z = 4

2. Find the value of k for which the equations kx - 2 y + z = 1, x - 2ky + z = -2, x - 2 y + kz = 1 have

(i) no solution

(ii) unique solution

(iii) infinitely many solution

3. Investigate the values of λ and μ the system of linear equations 2x + 3y + 5z = 9, 7x + 3y – 5z = 8, 2x + 3y + λ z = µ , have

(i) no solution (ii) a unique solution (iii) an infinite number of solutions.

Answers: