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Value of 'alpha' for which system of equ...

Value of `'alpha'` for which system of equations `x+y+z=1,x+2y+4z=alpha` and `x+4y+10 z=alpha^2` is consistent, are 1 (b) 3 (c) 2 (d) 0

A

1,2

B

`-1,2`

C

`1, -2`

D

`-1, -2`

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Knowledge Check

  • The values of alpha for which the system of equations x+y+z=1 x+2y+4z+alpha x+4y+10z=alpha^2 is consistent, are

    A
    `1,-2`
    B
    `-1,2`
    C
    1,2
    D
    None of these

  • The system of equations x-y+3z=4 x+z=2 x+y-z=0 has

    A
    A unique solution
    B
    Finitely many solution
    C
    Infinitely many solutions
    D
    None of the above

  • The system of lienar equations x-y+z=1 x+y-z=3 x-4y+4z=alpha has

    A
    a unique solution when `alpha=2`
    B
    a unique number when `alpha!=-2`
    C
    an infinite number of solutions when `alpha=2`
    D
    an infinite number of solutions, when `alpha=-2`