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Matrix as a product of elementary matrices

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data

    Sorry for the double post, I couldn't re-edit the topic on my earlier post.

    The assignment is to represent the following matrix as a product of elementary matrices:

    1 3 5
    3 10 11
    -2 -7 -7

    I reduced this matrix down to the identity matrix I using elementary row operations, which I recorded. I'll paste these here:

    1)row 2 = row2 - 3row1
    2)row 3 = row3 + 2row1
    3)row 3 = row3 + row2
    4)row 3 = -1*row3
    5)row 1 = row1 - 3row2
    6)row 1 = row1 - 17row3
    7)row 2 = row2 - 4row3

    The idea is now to represent each operation as an elementary matrix, and the product of the inverses of these matrices should give me my original matrix, correct?

    1 0 0
    3 1 0
    0 0 1

    1 0 0
    0 1 0
    0 -2 1

    1 0 0
    0 1 0
    0 -1 1

    1 0 0
    0 1 0
    0 0 -1

    1 3 0
    0 1 0
    0 0 1

    1 0 17
    0 1 0
    0 0 1

    1 0 0
    0 1 -4
    0 0 1


    the above matrices are the inverses of these row operations in elementary matrix form (I THINK!)(1-7 top to bottom). Here is the problem... when I multiply these matrices out (using matlab) I'm getting the same answer every time:

    1 3 5
    3 10 11
    0 -3 13

    the last row is clearly off, while the rest is right on... This is driving me crazy! Any help?
     
  2. jcsd
  3. Sep 8, 2009 #2
    First, I reduced the matrix to identity matrix and spotted one error:
    7) should be row2+4row3

    Also, you got wrong the inverse matrix of the 2) elementary matrix

    It should be:

    1 0 0
    0 1 0
    -2 0 1
     
  4. Sep 8, 2009 #3
    Thanks! How on earth did I miss that initially...
     
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