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Gaussian Elimination

  1. Jan 23, 2007 #1
    Question:

    solve by using gaussian elimination:

    3x - y + z = 1
    2x + 2y – 5z = 0
    5x + y – 4z = 7

    what i did:

    step 1: new row 1 = old row 1 – row 2, I got:

    x – 3y + 6z = 1
    2x + 2y – 5z = 0
    5x + y – 4z = 7

    step 2: new row 2 = old row 2 – (2 * row1) and new row 3 = old row 3 – (5 * row 1), I got:

    x – 3y + 6z = 1
    0 + 8y – 17z = -2
    0 + 16y – 34z = 2

    step 3: new row 3 = old row 3 * (1/2) I got:

    x – 3y + 6z = 1
    0 + 8y – 17z = -2
    0 + 8y – 16z = 1

    step 4: new row 3 = old row 3 – row 2, I got:

    x – 3y + 6z = 1
    0 + 8y – 17z = -2
    0 + 0 + z = 3

    the Real Answer:

    Gaussian elimination gives 0z = 6, ie, 0 = 6 which is clearly impossible.
    NO solutions.



    i obviously didn’t get that, and i would really appreciate it if someone could check whether i am going wrong somewhere or if my teacher is wrong

    thanx
     
    Last edited: Jan 23, 2007
  2. jcsd
  3. Jan 23, 2007 #2

    Dick

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    For one thing in step 3, 34/2=17 not 16. You are just making arithmetic errors.
     
  4. Jan 23, 2007 #3
    you know i did that question 3 times and i made that mistake three times how stupid of me lol!
    i was never meant to do maths
    thanx for your help!
     
  5. Jan 23, 2007 #4

    Dick

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    The same thing happens to me. You're welcome.
     
  6. Jan 23, 2007 #5

    mjsd

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    by the way, the ability to do maths is somewhat different from whether you are meticulous.

    the quick way to check whether a system of equations are solvable, find the determinant of the matrix, in this case the determinant of
    [tex]\begin{pmatrix}3&-1&1\\ 2&2&-5\\ 5&1&-4\end{pmatrix}[/tex]
    is actually 0 , ie. the matrix is non-invertible, so no solutions.
     
  7. Jan 23, 2007 #6
    yes you're right! thanx i'll find the determinant for the rest of the questions (we were actually taught that method - but i've just been winding my self up)
     
  8. Jul 26, 2009 #7
    3x - y + z = 1
    2x + 2y – 5z = 0
    5x + y – 4z = 7

    look by subtracting 2nd from 3rd it gives
    3x-y+z= 7

    so there a two similar equations
    3x - y + z = 1
    3x-y+z= 7

    so this question don't have an answer
     
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