The system of equations: `x+y+z=5`, `x+2y+3z=9` and `x+3y+lambdaz=mu` has a unique solution, if
(a) `lambda=5,mu=13`
(b) `lambda!=5`
(c)`lambda=5,mu!=13`
(d) `mu!=13`

Options

A. `lambda=5,mu=13`
B. `lambda ne 5`
C. `lambda=5, mu ne 13`
D. `mu ne 13`

Answer

B

Explanation

The system oif equations will have unique solution if
`{:[(1,1,1),(1,2,3),(1,3,lambda)]:} ne 0 rArrlambda -5 ne 0 rArr lambda ne 5`