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Homework Help: Linear Algebra-Uniqueness of rref

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data

    "Prove a specific rref matrix is unique"

    2. Relevant equations



    3. The attempt at a solution

    This is all I have on my review sheet for my next exam. I have the proof of the uniqueness of rref but how do you prove a specific rref matrix is unique ?

    say that's any nonsingular matrix in R^3
    Would appreciate any hints.

    Thanks,
    Roni.
     
  2. jcsd
  3. Mar 27, 2010 #2
    If the system is unique, we know it is nonsingular. What does a nonsingular rref matrix look like? It is a diagonal matrix with 1s in the diagonals or identity matrix.

    Also, if the nxn matrix is unique, the column vectors are linearly independent.
     
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