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A determinant containing a variable

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants?
    [x 2x 4 x ]
    [1 2 2x 1 ]
    [2x x-1 2 3x]
    [ 2 x+1 x+3 x-1]
    What are the different values of x?

    2. Relevant equations



    3. The attempt at a solution
    I've tried ellimination and by using cofactors. When fully computed, it will be a polynomial of the 4th degree, as one probably can see.
    Ellimination didn't make it simpler to factorize and cofactors just solved it until the polynomial popped up at the end-
     
  2. jcsd
  3. Jan 15, 2013 #2

    Mark44

    Staff: Mentor

    What did you get?
     
  4. Jan 15, 2013 #3
    8x4-22x3-22x2+47x+3
     
  5. Jan 15, 2013 #4

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    Is this your determinant?$$
    \left|\begin{array}{cccc}
    x & 2x & 4 & x \\
    1 & 2 & 2x & 1\\
    2x & x-1 & 2 & 3x\\
    2 & x+1 & x+3 & x-1
    \end{array}\right|$$
    If so, your last two terms should be ##44x+12##. Still, once you have the polynomial correct, you haven't said what you are supposed to do with it. It doesn't make sense to ask "what are the different values of ##x##".
     
  6. Jan 16, 2013 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The different values of x that give the determinant what property? That it be 0? That it not be 0?

     
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