Results 1 to 2 of 2

Math Help - Linear alg. question concerning elementary row operations

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    104

    Linear alg. question concerning elementary row operations

    Hi I have to prove this statement:
    Prove that if a matrix Q can be obtained from a matrix P by an elementary row operation, then P can be obtained from Q by an elementary matrix of the same type.
    What would the proof of this look like?
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    Quote Originally Posted by dannyboycurtis View Post
    Hi I have to prove this statement:
    Prove that if a matrix Q can be obtained from a matrix P by an elementary row operation, then P can be obtained from Q by an elementary matrix of the same type.
    What would the proof of this look like?
    Thanks
    Hi - Outlines of the prove
    1. Note/Show - Inverse of every type of row operation is also a row operation
    2. Use induction over number of row operations,n, needed for P->Q. Prove for the base case where n=1. You have to show that inverse of all three types of row operations restore the matrix to the original form.
    3. Once this is done just use the induction logic to complete the prove.

    I would assume this is a std way and can be found in most of the textbooks.
    Thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Elementary Row Operations
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 9th 2010, 04:44 AM
  2. Elementary row operations
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 1st 2009, 10:23 PM
  3. Elementary Row Operations
    Posted in the Advanced Algebra Forum
    Replies: 13
    Last Post: June 10th 2008, 11:34 AM
  4. Elementary row operations
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 17th 2007, 09:01 AM
  5. Elementary Row Operations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 17th 2007, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum