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