The set of all values of `lambda` for which the system of linear equations
`x - 2y - 2z = lambdax`
`x + 2y + z = lambday`
`-x -y = lambdaz`
has a non-trivial solution

Options

A. is an empty set
B. is a singleton set
C. contains two elements
D. contains more than two elements

Answer

3

Explanation

System has non-initial solution
`:. |{:(lambda-2,,2,,-1),(2,,-3-lambda,,2),(-1,,2,,-lambda):}|=0`
`rArr (lambda -2)(3lambda +lambda^(2)-4)-2(-2lambda +2) -1(4-3-lambda)=0`
`rArr (lambda-2)(lambda-1)(lambda+4)+4(lambda-1)+(lambda-1)=0`
`rArr (lambda-1)(lambda^(2) +2lambda-8+5) =0`
`rArr (lambda-1)(lambda^(2) +2lambda-3)=0`
`rArr (lambda-1)^(2)(lambda+3)=0`