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The system of linear equations x+lambday...

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) exactly three values of `lambda` .

A

infinitely many values of ` lambda`

B

exactly one value of `lambda`

C

exactly two values of `lambda`

D

exactly three values of `lambda`

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The correct Answer is:
D
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE MAIN ARCHIVE
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  2. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

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  3. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  4. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

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  5. about to only mathematics

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  6. Let A be a 3xx3 matrix such that A^2-5A+7I=0 then which of the stateme...

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  7. If {:A=[(-4,-1),(3,1)]:}, then the determint of the matrix (A^2016-2A^...

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  8. The set of all values of lambda for which the system of linear equ...

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  9. if A=[(1,2,3),(2,1,-1),(a,2,b)] is a matrix satisfying A A'=9l(3,) fin...

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  10. if the value of the determinant |{:(a,,1,,1),(1,,b,,1),(1,,1,,c):}| ...

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  11. If A=[(0,-1),(1,0)] , then which one of the following statements is n...

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  12. If A is a 3 x 3 matrix such that |5-adjA|=5 , then |A| is equal to ...

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  13. If |(x^2+x,x+1,x-2),(2x^2+3x-1,3x,3x-3),(x^2+2x+3,2x-1,2x-1)|=ax-12 t...

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  14. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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  15. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

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  16. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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  17. The number of values of k, for which the system of eauations: (k+1)x...

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  18. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

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  19. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  20. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

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