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For which value (s) of lambda, do the pa...

For which value (s) of `lambda`, do the pair of linear equations `lambdax + y = lambda^(2)` and `x + lambda y = 1 ` have
(i) no solution ? (ii) infinitely many solutions ?
(iii) a unique solution ?

Answer

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For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have no solution?

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Knowledge Check

  • The value of k, for which the pair of linear equations k x + y = k^(2) and x + k y = 1 has infinitely many solution, is :

    A
    `pm 1`
    B
    `-2`
    C
    `-1`
    D
    2

  • The system of linear equations x + lambda y-z =0, lambdax-y -z =0, x + y -lambda z =0 has a non-trivial solution for

    A
    infinitely many values of `lambda`
    B
    exactly one value of `lambda`
    C
    exactly two values of `lambda`
    D
    exactly three values of `lambda`

  • The value of k, for which the pair of linear equations kx+y=k^(2) and x + ky = 1 has infinitely many solution, is:

    A
    `+-1`
    B
    1
    C
    -1
    D
    2

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    For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have infinitely many solutions?

    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

    The set of all values of lambda for which the systme of linear equations x-2y-2z = lambda x, x +2y +z = lambda y " and "-x-y = lambdaz has a non-trivial solution.

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