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Homework Help: Finding a determinant

  1. Jan 29, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the determinant of the following matrix:


    4.....0.....1
    19...1....-3
    7.....1.....0


    I chose the 1st row to do the operations on.

    4 [(1*0) - 1*(-3)] + 1 [19*1 - 7*1]

    = 4[0 - (-3)] + 1[12]
    =12 + 12
    =24




    I can't see any mistakes in that, but it's apparently wrong. The answer is supposed to be 0. Here's the thing, for some rows/colums, the answer comes out to be 24, while for other rows/colums, the answer is 0. Shouldn't it not matter which row/column you choose? So why am I getting different answers?




    For example, if I choose the 3rd column...


    1 [19 - 7] - 3 [4 - 0]
    = 12 - 12
    = 0


    So why am I getting different answers?
     
  2. jcsd
  3. Jan 29, 2010 #2

    berkeman

    User Avatar

    Staff: Mentor

    Are you familiar with the method of visualizing the diagonal multiplications? That's the way I prefer to do it, and it does give an answer of zero.

    See the 3x3 matrix determinant example part-way down this page:

    http://en.wikipedia.org/wiki/Determinant

    .
     
  4. Jan 29, 2010 #3

    Mark44

    Staff: Mentor

    I get a determinant of 24 in two ways: expanding the first row; expanding the 3rd column. There is a sign error in your work in expanding the third column.
    It should be
    1 [19 - 7] - (-3) [4 - 0]
    = 12 + 12
    = 24
     
  5. Jan 29, 2010 #4

    berkeman

    User Avatar

    Staff: Mentor

    Ack! I dropped that "-" sign as well. Thanks Mark.
     
  6. Jan 29, 2010 #5

    Mark44

    Staff: Mentor

    Happens to us all... leastwise it happens to me!
     
  7. Jan 29, 2010 #6
    The answer given is 0, even though 24 also works, as we have seen.

    So what's the deal? Are there two determinants?
     
  8. Jan 29, 2010 #7

    Mark44

    Staff: Mentor

    A matrix has only one determinant, so either the given answer is wrong or the matrix you showed us is different from the one in your book's problem.
     
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