# The system of linear equationsx +λy −z = 0 λx − y − z = 0 x + y − λz = 0has a non-trivial solution for : Option 1) infinitely many values of λ.   Option 2) exactly one value of λ.   Option 3) exactly two values of λ.   Option 4) exactly three values of λ.

As we learnt in

Cramer's rule for solving system of linear equations -

When   and  ,

then  the system of equations has infinite solutions.

- wherein

and

are obtained by replacing column 1,2,3 of  by   column

Option 1)

infinitely many values of λ.

This option is incorrect.

Option 2)

exactly one value of λ.

This option is incorrect.

Option 3)

exactly two values of λ.

This option is incorrect.

Option 4)

exactly three values of λ.

This option is correct.

Solution Video

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