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Solving via Gaussian Elimination

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve the following system of equations using Gaussian Elimination:
    -2a+5c=1
    a+2b-c=2
    3a-2b=3

    2. Relevant equations
    N/A

    3. The attempt at a solution
    Augmented matrix
    (-2 0 5 | 1) R2 → R2 +R1/2
    (1 2 -1 | 2) R3 → R3 - 3R2
    (3 -2 0 | 3)

    (-2 0 5 | 1) Swap R2 and R3
    (0 2 3/2 | 5/2)
    (0 -8 0 | -3)

    (-2 0 5 | 1) R2 → -R2/4
    (0 -8 0 | -3)
    (0 2 3/2 | 5/2)

    (-2 0 5 | 1) R3 → R3-R2
    (0 2 0 | 3/4)
    (0 2 3/2 | 5/2)

    (-2 0 5 | 1) R3 → R3*10/3
    (0 2 0 | 3/4)
    (0 2 3/2 | 5/2)

    (-2 0 5 | 1) R1 → R1-R3
    (0 2 0 | 3/4)
    (0 0 5 | 7/12)

    (-2 0 0 | 5/12)
    (0 2 0 | 3/4)
    (0 0 5 | 7/12)

    therefore a=-5/24, b=3/8 and c=7/60

    The problem is a and c satisfy the equation but b does not, not sure what i've done wrong especially since a and c both work. Any help?
     
  2. jcsd
  3. Oct 19, 2011 #2

    lanedance

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    Homework Helper

    -2a+5c=1
    -2(-5/24) + 5(7/60) = 10/24+30/60 = 5/12+6/12

    so a & c do not work, I would go back and check each of your steps
     
  4. Oct 19, 2011 #3

    verty

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    You may not do two operations simultaneously.
     
  5. Oct 19, 2011 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    ?? He didn't.

    Your error is here. R3- 3R2, in the third column, would be 0-3(-1)= 3, not 0.

     
  6. Oct 19, 2011 #5
    Ahh thanks can't believe I didn't notice it, all works nicely now.
     
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