Question

The existence of the unique solution of the system of equations:

x + y + z = λ

5x – y + μz = 10

2x + 3y – z = 6 depends on

A. μ only

B. λ only

C. λ and μ both

D. neither λ nor μ

Answer 1

Correct option is A. μ only

The given system of linear equation :-

x + y + z = λ

5x – y + μz = 10

2x + 3y – z = 6

The matrix equation corresponding to the above system is :-

For the existence of the unique solution, the value of |A| must be equal to 0.

Hence the existence of the unique solution merely depends on the value of μ.