Results 1 to 3 of 3

Math Help - Proof help matrices

  1. #1
    Junior Member
    Joined
    Dec 2006
    Posts
    43

    Proof help matrices

    hi, i'm practicing proofs for an upcoming test regarding systems of linear equations, matrices, and Gaussian elimination. i was wondering if anyone could show me how to do the following that i found in my textbook in case i'm asked to do a similar one:

    Prove that if more than one solution in a system of linear equations exists, then an infinite number of solutions exists. (Hint: Show that if x1 and x2 are different solutions to AX = B, then x1 + C(x2 - x1) is also a solution for every real number c. Also, show that these solutions are different).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Suppose we use x & y as two different solutions to AX=B.
    Then A[x+c(y-x)]=Ax+cAy-cAx=B+cB-cB=B for every c.
    Thus we have infinitely many solutions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2006
    Posts
    43
    Thanks. Are there any particular theorems that proof those statements, though?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proof of similar matrices
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: June 30th 2011, 07:52 PM
  2. Basis, set of matrices, proof...
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 27th 2011, 09:06 AM
  3. Proof for inverse matrices
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 11th 2010, 07:12 PM
  4. Proof- Invertible Matrices
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 6th 2009, 12:54 PM
  5. Proof of equivalent matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 9th 2008, 03:29 PM

Search Tags


/mathhelpforum @mathhelpforum