The number of distinct real values of ` lamda ` for which the system of linear equations ` x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z ` has non - trival solution.

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

`(1-lambda) x + y + z = 0, x + (1- lambda) y + x = 0 ,`
For non - trivial soluiton
`|{:(1-lambda,1,1),(1,1-lambda,1),(1,1,1-lambda):}| rArr (1-lambda){(1-lambda)^(2) - 1} + { 1 - (1- lambda)} = 0 `
`rArr (1-lambda)^(3) - (1- lambda) + lambda + lambda = 0 rArr 1 - 3 lambda + 3lambda^(2) - lambda^(3) -1 + 3 lambda = 0`
`rArr lambda^(3) - 3lambda^(2) = 0 " " rArr lambda = 0 , 3`