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System of equations

  1. Oct 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Under what condition will the following system have a unique solution?

    x -y +2z = 1
    ax -ay +4z = 2a
    x +y +az = 4

    Note: a is a parameter.

    3. The attempt at a solution
    I know I'm supposed to solve by turning this into the identity matrix by I really have no idea where to start. Hellp would be much appreciated.
  2. jcsd
  3. Oct 11, 2013 #2


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    Science Advisor
    Gold Member

    Rewrite the equation in matrix form:

    1 -1 2 x 1
    a -a 4 * y = 2a
    1 1 a z 4

    This system is has a unique solution if the matrix on the LHS has an inverse.

    From your (3) it seems that you are to use Gaussian elimination:

    Depending on how you set this up it can provide the inverse matrix and the solution.
  4. Oct 11, 2013 #3
    Can I ignore the right side of all the equations in order to find the inverse?
  5. Oct 11, 2013 #4


    Staff: Mentor

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