Results 1 to 2 of 2

Math Help - [Reduced] Column Echelon Form

  1. #1
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3

    [Reduced] Column Echelon Form

    I'm trying to understand this a little better.

    If we have a n\times n matrix, \left[\begin{array}{cccc}a_{11}&a_{12}&\cdots&a_{1n}\\a_  {21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&  a_{nn}\end{array}\right], would the CEF have the form \left[\begin{array}{ccccc}1&0&0&\cdots&0\\a_{21}&1&0&\cd  ots&0\\ \vdots&\vdots&\ddots&\ddots&\vdots\\a_{(n-1)1}&a_{(n-1)2}&\cdots&1&0\\a_{n1}&a_{n2}&a_{n3}&\cdots&1\end  {array}\right]??

    And would the RCEF of this matrix be I_{n\times n}??\

    I'd appreciate any clarification!

    --Chris
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by Chris L T521 View Post
    I'm trying to understand this a little better.

    If we have a n\times n matrix, \left[\begin{array}{cccc}a_{11}&a_{12}&\cdots&a_{1n}\\a_  {21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&  a_{nn}\end{array}\right], would the CEF have the form \left[\begin{array}{ccccc}1&0&0&\cdots&0\\a_{21}&1&0&\cd  ots&0\\ \vdots&\vdots&\ddots&\ddots&\vdots\\a_{(n-1)1}&a_{(n-1)2}&\cdots&1&0\\a_{n1}&a_{n2}&a_{n3}&\cdots&1\end  {array}\right]??

    And would the RCEF of this matrix be I_{n\times n}??\

    I'd appreciate any clarification!

    --Chris
    i guess by "column echelon form" of a matrix A you mean the row echelon form of A^T. i'm saying this because row echelon form is what we normally use. well, the answer to your question

    is "yes" only if your (square) matrix is invertible. for example \begin{bmatrix}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 0 \end{bmatrix} is also in column echelon form. besides your matrix can be any m \times n matrix.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 4th 2011, 03:06 AM
  2. Row/Column space and reduced row echelon form.
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: April 12th 2011, 05:42 PM
  3. row reduced echelon form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 11th 2009, 07:46 PM
  4. Huge Row Reduced Echelon Form Problem
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: February 24th 2009, 04:53 PM
  5. Replies: 7
    Last Post: December 24th 2007, 09:17 PM

Search Tags


/mathhelpforum @mathhelpforum