Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By zhandele

Math Help - urgent.-reduced row echelon form R,.....S

  1. #1
    n22
    n22 is offline
    Member
    Joined
    May 2013
    From
    england
    Posts
    100

    urgent.-reduced row echelon form R,.....S

    Hi does anyone know how to do this question? im unsure about the theory as well.thanks.
    If A is a 7x5 matrix with reduced row echelon form R and B is a 4x6 matrix with reduced row echelon form S. Which of the following statements are always true.

    R has at least one zero row/ S has at least one zero row/R has at least one column without a leading one /S has at least one column without a leading one /The system Ax=b has at least one solution for all b which is an element of R7/The system Bx=0 has infinitely many solutions .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2012
    From
    Normal, IL USA
    Posts
    158
    Thanks
    25

    Re: urgent.-reduced row echelon form R,.....S

    A 7x5 matrix has 7 rows, five columns. Row Reduction constructs a stairstep pattern. If the columns are linearly independent, the RREF will show a diagonal of ones with zeroes above and below. Note that this is the "most common case," in the sense that if you generate a random matrix it's very unlikely this is what you'll get.

    I can't seem to get the latex to work right now, but R will "almost certainly" have a 1 in the top left, and a diagonal of 1's, everything else 0. There will be two rows of zeroes at the bottom.

    You need to consider other cases. Your answers should become clear.

    You say you're not so clear on the theory? The best I can think of now is this: make sure you understand why the RREF has the same solution set as the original matrix. If that's clear, the rest should follow.
    Last edited by zhandele; June 10th 2013 at 07:46 PM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 4th 2011, 04:06 AM
  2. row reduced echelon form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 11th 2009, 08:46 PM
  3. Huge Row Reduced Echelon Form Problem
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: February 24th 2009, 05:53 PM
  4. [Reduced] Column Echelon Form
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 23rd 2008, 08:45 PM
  5. Replies: 7
    Last Post: December 24th 2007, 10:17 PM

Search Tags


/mathhelpforum @mathhelpforum