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Math Help - Determinant problem

  1. #1
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    Determinant problem

    The fuction D(t) is the determinant of a 4x4 matrix:

    D(t) = |1 2 3 4|
    |-1 0 -2 0|
    |4 3 2 1|
    |1 1 2 t|

    Find the determinant D(t) and find the value t0 which gives D(t0) = 2/7

    Thanks!
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  2. #2
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    Quote Originally Posted by gralla55 View Post
    The fuction D(t) is the determinant of a 4x4 matrix:

    D(t) = |1 2 3 4|
    |-1 0 -2 0|
    |4 3 2 1|
    |1 1 2 t|

    Find the determinant D(t) and find the value t0 which gives D(t0) = 2/7

    Thanks!
    You must know what to do to evaluate determinants of this kind if you were given this question to solve, so : what have you done so far and where are you stuck?

    Tonio
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  3. #3
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    You could use the Laplace expansion, If you are confused about the method to be used for evaluating det of this 4x4 matix. Firstly, you choose any element a_{ij}=1 or, if lacking, a_{ij} \neq 0 . Then you use a_{ij} as a pivot, apply elementary row [column] operations to put 0s in all other positions in column j [row i]. Then expand the determinant cofactors of column j [row i]. Let's see how you go.
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  4. #4
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    Ok thanks, I got the determinant to be 25. Still, how do I find the value t0 which gives D(t0) = 2/7 ?
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  5. #5
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    Isn't there any program which solves this type of problem? I just need the answer for a t0 which gives D(t0) = 2/7, no explanation needed :P
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  6. #6
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    Quote Originally Posted by gralla55 View Post
    Isn't there any program which solves this type of problem? I just need the answer for a t0 which gives D(t0) = 2/7, no explanation needed :P
    What you need is a way to write D(t) as a polynomial function of t.
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  7. #7
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    "What you need is a way to write D(t) as a polynomial function of t."

    Just realized that! But how? I have 1 hour to solve this, and I don't have my books here so I kinda need some help :P Would very much appreciate it!
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  8. #8
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    Just find the formula for calculating determinants of 4x4 matrices and apply it.
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  9. #9
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    Sure, but I don't have my books and that's why I'm asking :P Anyone? I have very little time left =( (10 hours)
    Last edited by gralla55; February 18th 2010 at 03:28 PM.
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