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Homework Help: Augmented Matrix proof

  1. Feb 27, 2010 #1
    Hi,

    i have just started with learning linear algebra ,so please bear with me. It seems like a quite simple question:

    Let [A b] an augmented matrix. Prove that if its reduced row echelon form (rref) is [R c] ,then R is the rref of A.
     
    Last edited: Feb 27, 2010
  2. jcsd
  3. Feb 27, 2010 #2

    HallsofIvy

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    What is the defintion of "reduce row echelon form"?
     
  4. Feb 27, 2010 #3
    First ,thanks for replying.

    rref is the simplest and most suitable form for Gaussian Elimination obtained by applying elementary row operations.(interchange ,scaling ,or row addition)

    Following are requirements :
    1.Every nonzero row lies above each zero row.
    2.The leading entry of a nonzero row lies in a column to the right of the column containing the leading entry of any preceding row.
    3.If a column contains the leading entry of some row ,then all the other entries in that column are zero.
    4.The leading entry of each nonzero row is 1.

    ex:

    1 0 * * 0 0 *
    0 1 * * 0 0 *
    0 0 0 0 1 0 *
    0 0 0 0 0 1 *
    0 0 0 0 0 0 0 (* represents arbitrary real number)

    A row with no other entry except zero is referred to zero row ,vice versa.
     
    Last edited: Feb 27, 2010
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