The system of linear equations`x+lambday-z=0``lambdax-y-z=0``x+y-lambdaz=0`has a non-trivial solution for :(1) infinitely many values of `lambda`.(2) exactly one value of `lambda`.(3) exactly two values of `lambda`.(4) exactlythree values of `lambda`.A. infinitely many value of `lambda`B. exactly one value of `lambda`C. exactly two values `lambda`D. exactly three values of `lambda`

The system of linear equations`x+lambday-z=0``lambdax-y-z=0``x+y-lambd

1.	The system of linear equations`x+lambday-z=0``lambdax-y-z=0``x+y-lambdaz=0`has a non-trivial solution for :(1) infinitely many values of `lambda`.(2) exactly one value of `lambda`.(3) exactly two values of `lambda`.(4) exactlythree values of `lambda`.A. infinitely many value of `lambda`B. exactly one value of `lambda`C. exactly two values `lambda`D. exactly three values of `lambda`
Answer» Correct Answer - D The given system of equations will have infinitely many non-trivial solutions, if `{:abs((1,lambda,-1),(lambda,-1,-1),(1,1 ,lambda))=0:}` `rArr (lambda +1)-lambda (-lambda^2+1)-1(lambda+1)=0` `rArr lambda^3-lambda =0 rArr lambda(lambda^2-1)-0rArrlambda=0,1,-1`

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