Question

The system of equations:

x + y + z = 5

x + 2y + 3z = 9

x + 3y + λz = μ

has a unique solution, if

A. λ = 5, μ = 13

B. λ ≠ 5

C. λ = 5, μ ≠ 13

D. μ ≠ 13

Answer 1

Correct option is B. λ ≠ 5

The given system of linear equations is :-

x + y + z = 5

x + 2y + 3z = 9

x + 3y + λz = μ

The matrix equation corresponding to the above system is

For the existence of a unique solution |A| ≠ 0

\(\therefore\) λ - 5 ≠ 0

λ ≠ 5