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Homework Help: Solving a set of equations

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that the following equations can be solved for any a:
    ax1 + 2x2 + ax3 = 5a
    x1 + 2x2 + (2-a)x3 = 5
    3x1 + (a+2)x2 + 6x3 = 15

    2. The attempt at a solution
    I thought I would do gaussian elimination to get it into reduced form (in a coefficient matrix), and see where I can go from there. But I don't know how to do Gaussian elimination because the coefficient of a certrain x1 is a...

    Can anybody give a hint?
  2. jcsd
  3. Oct 6, 2009 #2


    Staff: Mentor

    Just use Gaussian elimination. For starters, add row 1 to -a times row 2, and add -3 times row 1 to a times row 3. That will eliminate the first entries in the 2nd and 3rd rows. Continue until you get the system in row-echelon form.

    Alternatively, you can divide row 1 by a, but in doing so, you are tacitly assuming that a != 0.
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