1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Augmented matrix linear algebra

  1. Oct 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Given the system whose augmented matrix is
     1 1 1 1 
     1 −1 0 a 
     0 1 b 0 
    Determine (if possible) conditions on a and b such that this system has (a) no solution (b) many solutions (c) a unique solution.

    2. Relevant equations

    -Row reduction
    -No solution: row of zero
    -Many solutions: one or more free variables
    -Unique solution: pivot in every column

    3. The attempt at a solution

    I tried to do it, but my answers were wrong. The good answers are a) b=1/2, a≠1 b) b=1/2, a=1 c) b≠1/2.

    I tried to reduce the matrix and I had:

     0 0 1-2b 1-3a 
     1 0 b 2a 
     0 1 b a 

    Can someone explain how to reduce the matrix properly or what am I doing wrong?
  2. jcsd
  3. Oct 2, 2013 #2


    Staff: Mentor

    Right off the bat I swapped the 2nd and 3rd rows. After that, I row reduced to get a matrix in echelon form. I get the same answers as your "good" ones.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted