The system of linear equations

Question:

The system of linear equations

$x+\lambda y-z=0$

$\lambda x-y-z=0$

$x+y-\lambda z=0$

has a non-trivial solution for :

  1. exactly three values of $\lambda$.

  2.  infinitely many values of $\lambda$.

  3. exactly one value of $\lambda$.

  4. exactly two values of $\lambda$.


Correct Option: 1,

Solution:

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