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What does 'write A as a product of 4 elementary matrices' mean?

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data
    So, if the problem asks...

    Find the elementary matrices such that the respective matrix equation holds...what do I do?

    [_ _ _] [4 4 -1] [4 4 -1 ]
    [_ _ _] [4 -1 -5] = [4 -1 -5]
    [_ _ _] [-4 1 4] [-12 3 12]

    Does this mean to find a matrix that when multiplied with the other gives the matrix on the other side of the equal sign?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 11, 2009 #2
    i think that is what it means..
     
  4. Mar 12, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This problem assumes that you know what an "elementary" matrix is!

    An elementary matrix is one that corresponds to a "row operation". Multiplying any matrix by that elementary matrix is the same as doing the corresponding row operation to the matrix.

    There are three kinds of row operations:
    a) Swap two rows of the matrix.
    b) Multiply every number in one row by the same number.
    c) Add a multiple of one row to another.

    You get the elementary operation corresponding to a row operation just by performing that row operation on the identity matrix.

    What row operation will change the matrix on the left into the matrix on the right? Although your title says "4 elementary matrices", for this problem onlyone is required.
     
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