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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

    Mark44

    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.
     
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