Results 1 to 2 of 2

Math Help - Solutions of Linear Systems: Matrix Algebra

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    7

    Solutions of Linear Systems: Matrix Algebra

    Let A be a 4x3 matrix and let b and c be two vectors in R^4. We are told that the system Ax=b has a unique solution. What can you say about the number of solutions of the system Ax=c?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    A "4 by 3" matrix maps a 3 vector into a 4 vector. More specifically, it maps all of R^3 to a subspace of R^4, of dimension 3 or less. If the dimension were less than 3 then A would have non-trivial kernel and more than one vector would be mapped to a specific vector in that subspace. Saying that Ax= b has a solution means that b is in that subspace. Saying that Ax= b has a unique solution means that a unique vector is mapped into every member of that subspace. So there are two possibilities for the number of solutions of Ax= c depending upon whether c happens to be in that subspace or not.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solutions of Linear Systems II
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 6th 2011, 07:22 AM
  2. Solutions of Linear Systems III
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 6th 2011, 07:17 AM
  3. Solutions of Linear Systems I
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 5th 2011, 10:57 PM
  4. [SOLVED] Solutions of four linear systems
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 14th 2010, 12:42 PM
  5. Periodic Solutions in Non-Linear systems
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: December 9th 2009, 08:50 AM

Search Tags


/mathhelpforum @mathhelpforum