Results 1 to 2 of 2

Math Help - Linear Algebra; prove the theorems on left and right inverses.

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    54

    Linear Algebra; prove the theorems on left and right inverses.

    Prove that if the matrix A has a right inverse, then for each b
    the equation Ax = b has at least one solution. If A has a left inverse,
    then that equation has at most one solution.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by mathwizard View Post
    Prove that if the matrix A has a right inverse, then for each b
    the equation Ax = b has at least one solution.
    let AB=I, with I identity matrix. then ABb=Ib=b, i.e. x=Bb satisfies Ax=b. so there's at least one solution.

    If A has a left inverse, then that equation has at most one solution.
    let CA=I, and suppose that Ax=Ay=b. then x=Ix=CAx=CAy=Iy=y. so Ax=b has at most one solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Right and Left Square matrix inverses
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: November 30th 2010, 09:23 AM
  2. left and right inverses of functions
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 29th 2010, 10:07 PM
  3. Linear algebra : base, vector space, prove that.
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 20th 2009, 10:04 PM
  4. linear algebra inverses
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 13th 2007, 07:50 AM
  5. Linear Algebra Proof - Prove that when A+D=0, D is unique.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 4th 2007, 05:28 PM

Search Tags


/mathhelpforum @mathhelpforum