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Math Help - use cramer's rule to determine what values of (variable) yield.....

  1. #1
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    use cramer's rule to determine what values of (variable) yield.....

    Ok well.......

    the system:

    x- y+ 3z= -8
    2x+ 3y- z= 5
    3x+ 2y+ 2kz= -3k

    So using cramer's rule i first had to find the determinants.

    They are as follows:

    D=10k-10
    Dx= -14k-14
    Dy= 21k-21
    Dz= -15k+15

    Ok, well those are the determinants.

    Now i am supposed to use Cramer's Rule to determine what value(s) oh k yield............

    a)no solution?
    b)exactly on solution?
    c)infinitely many solutions?



    I thank you all in advanced
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  2. #2
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    Quote Originally Posted by Danktoker View Post
    Ok well.......

    the system:

    x- y+ 3z= -8
    2x+ 3y- z= 5
    3x+ 2y+ 2kz= -3k

    So using cramer's rule i first had to find the determinants.

    They are as follows:

    D=10k-10
    Dx= -14k-14
    Dy= 21k-21
    Dz= -15k+15

    Ok, well those are the determinants.

    Now i am supposed to use Cramer's Rule to determine what value(s) oh k yield............

    a)no solution?
    b)exactly on solution?
    c)infinitely many solutions?



    I thank you all in advanced

    If \Delta\neq 0\iff k\neq 1 then there's a unique solution, given (this is Cramer's Rule) by \begin{pmatrix}\frac{\Delta_x}{\Delta}\\{}\\\frac{  \Delta_y}{\Delta}\\{}\\\frac{\Delta_z}{\Delta}\end  {pmatrix} .

    If k=1 then bringing the augmented matrix into echelon form we get that there are infinite solutions.

    Tonio
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  3. #3
    Junior Member
    Joined
    Mar 2010
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    Hi Tonio Thank you very much for the reply.

    Just curious about how those deltas work, we have never talked about them.
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