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Homework Help: Matrices help!

  1. Oct 13, 2005 #1
    Hi, I've just been given a set of revision questions for matrices and I'm having problems with the following question:


    My task is to find the general solution of this system (if there is any). Do I start off by reducing it to row echelon form and then reduced row echelon?

    My first step would be to divide the first line by 3 to get a 1 on the far left...but that would mean I would have fractions as well which makes everything so 'messy.' Is that the correct first step to this question? :confused:

    Help and advice appreciated! Thank you!
    Last edited by a moderator: Apr 21, 2017
  2. jcsd
  3. Oct 13, 2005 #2
    I would start by multiplying the 2nd line by -1 and adding it to the 4th line.
  4. Oct 13, 2005 #3
    Ok I've given it a go and I got the answer:

    1 0 1 2 | 1
    0 1 -1 -2 | 0
    0 0 0 0 | 0
    0 0 0 0 | 0

    So that gives me no solution?....:confused: Can someone check if that's right. Thank you!! :biggrin:
  5. Oct 13, 2005 #4


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    Staff Emeritus
    Science Advisor
    Gold Member

    Looks correct to me. The matrix is singular, so there isn't a solution.
  6. Oct 13, 2005 #5
    Oh thanks! :biggrin: I know how to attempt other similar questions in my notes now.

    I've also got two more questions to ask, if that's ok :uhh:

    1) How do you determine a matrix is an elementary matrix? For example if you were given:

    1 0 0
    0 1 9
    0 0 1

    Is this an elementary matrix? :confused:

    2) I don't understand the wording of the following question:


    Does it mean its already in the echelon form so I don't have to do anything apart from just solving it for the variables? Or do I still have to put it into reduced echelon form?

    Sorry for being such a pain and thank you for taking time to read my post :smile:
    Last edited by a moderator: Apr 21, 2017
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