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Matrix determinant

  1. Nov 19, 2006 #1
    I have just tried to solve this problem and just wondering if I am right!

    1) Compute the determinant of the matrix A
    -1 -1 1
    x^2 y^2 z^2
    0 -1 0
    and find all real numbers x,y, and z such that A is not invertible.

    Okay so I found that the det=-z^2-x^2
    So when the matrix is invertible the determinant is zero!


    Can I say that matrix is invertible when z^2=-x^2?
    So my question from here is would I just list numbers that would make the det zero? And how would I find y?
  2. jcsd
  3. Nov 19, 2006 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Assuming you meant "not" invertible, your work looks right. There's a little bit more to do, though.

    If you mean just write down examples, then no. You need to write down the set of all possibilities! But, if you can prove that there are only finitely many possibilities, then writing them all down is good enough.

    You choose y so that the equation is satisfied. (hint: it's easy. You're probably overthinking it)
  4. Nov 19, 2006 #3
    Sorry not following with the last part!
    You choose y so that the equation is satisfied??
    U mean I substitute y in for x or somethin!
  5. Nov 19, 2006 #4


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    Homework Helper

    Since the determinant doesn't depend on y, y can be any real number.

    Hurkyl probably meant something like: S = {(x, y, z) E R^3 : z^2 = - x^2 & y E R }.
  6. Nov 19, 2006 #5
    ahhh okay that helps... thanks!
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