Find the real values of `lambda` for which the following system of linear equations has non-trivial solutions. Also, find the non-trivial solutions. `2lambdax-2y+3z=0` `x+lambday+2z=0` `2x+lambdaz=0`

Explanation

The given system of equations will have nontrivial solution if

`abs([2lambda,-2,3],[1,lambda,2],[2,0,lambda])`



`2lambda(lambda^2)+2(lambda−4)+3(-2lambda)=0
`

`2lambda(lambda)+2(lambda-2)+3(-2lambda)=0`

`2lambda^3-4lambda-8=0`

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