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The system of linear equations x+lambd...

The system of linear equations
`x+lambday-z=0`
`lambdax-y-z=0`
`x+y-lambdaz=0`
has a non-trivial solution for

A

exactly one-value of `lambda`

B

exactly two values of `lambda`

C

exactly three values of `lambda`

D

infinitely many values of `lambda`

Text Solution

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The correct Answer is:
C
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ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
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  4. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  6. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  9. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  10. If the trivial solution is the only solution of the system of equation...

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  11. The number of values of k, for which the system of equations (k""+"...

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  12. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

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  13. The set of the all values of lamda for which the system of linear equa...

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  14. Which of the following values of alpha satisfying the equation |(1+alp...

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  15. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

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  16. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

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  17. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

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  18. If S is the set of distinct values of ' b for which the following syst...

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