1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra question

  1. Jun 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Quote from my textbook:

    "The linear system Ax=b is consistent if and only if the number of nonzero rows of the augmented matrix [U| c], equals the number of nonzero rows in U."

    [U,c] is the rref of [A,b]


    2. Relevant equations



    3. The attempt at a solution

    I understand "only if" but not "if". "Only if" is true since the elementary row operations do not affect the solutions to the system and it is clear that a linear combination of zeros cannot equal a nonzero number. Can someone help me with "if"?
     
  2. jcsd
  3. Jun 16, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    number of nonzero rows in U is the rank of U,r(U)
    the no. of nonzero rows of [U|c] is the rank of that matrix,r(U|c)

    For a system of eq'ns to be constisent

    [tex]r(U)=r(U|c) \leq n[/tex]

    n= no . of rows
     
  4. Jun 18, 2008 #3
    Thanks for responding to my question!

    Unfortunately, I am still confused. It seems like that just restated my question using the word "rank".


    I think the quote I gave came from a proof of this statement actually...
     
  5. Jun 18, 2008 #4

    rock.freak667

    User Avatar
    Homework Helper

    well saying "if and only if", like restricting the statement so that the statement will be true when that condition is satisfied.
     
  6. Jun 18, 2008 #5
    I figured it out. Thanks for your help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear algebra question
Loading...