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Math Help - Matrices/Determinant problem

  1. #1
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    Matrices/Determinant problem

    Okay, so I had to row reduce the matrix below to upper-triangular form in order to find the determinant.

    [0, 0, 2, 0, 0]
    [2, 0, 58, 96, -1]
    [2, 1, 58, 96, -1]
    [0, 0, 2, -1, 0]
    [1, 0, 58, 96, 2]

    Row-reducing it to upper-triangular form, I wound up with:
    [1, 0, 29, 48, -1/2]
    [0, 1, 0, 0, 0]
    [0, 0, 1, 0, 0]
    [0, 0, 0, 1, 0]
    [0, 0, 0, 0, 3/2]

    I know that to calculate the determinant of an n by n upper-triangular matrix, all you do is multiply the entries along the diagonal. However, when I found the determinant of the first matrix using cofactors, I got -10. Multiplying the entries along the diagonal of the row-reduced upper triangular form, I got 3/2. Am I doing something wrong here? I've done out the row-reduction several times, and I keep getting a determinant of 3/2.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by buckaroobill View Post
    Okay, so I had to row reduce the matrix below to upper-triangular form in order to find the determinant.

    [0, 0, 2, 0, 0]
    [2, 0, 58, 96, -1]
    [2, 1, 58, 96, -1]
    [0, 0, 2, -1, 0]
    [1, 0, 58, 96, 2]

    Row-reducing it to upper-triangular form, I wound up with:
    [1, 0, 29, 48, -1/2]
    [0, 1, 0, 0, 0]
    [0, 0, 1, 0, 0]
    [0, 0, 0, 1, 0]
    [0, 0, 0, 0, 3/2]

    I know that to calculate the determinant of an n by n upper-triangular matrix, all you do is multiply the entries along the diagonal. However, when I found the determinant of the first matrix using cofactors, I got -10. Multiplying the entries along the diagonal of the row-reduced upper triangular form, I got 3/2. Am I doing something wrong here? I've done out the row-reduction several times, and I keep getting a determinant of 3/2.
    The determinant of this matrix is -10.

    Review what happens as you reduce the matrix to upper triangular form in
    the light of what is in the attachment to this post.

    RonL
    Attached Thumbnails Attached Thumbnails Matrices/Determinant problem-gash.jpg  
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