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Nonhomogeneous system of linear equations

  1. May 19, 2012 #1
    Hi all,

    How do u go about doing this question?

    x - 2y +z =4
    y- z =3
    (a^2 - a - 2)z = a+1

    Determine values of a for which the system has no solution, one solution and many solutions

  2. jcsd
  3. May 19, 2012 #2


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    Hey Stephen and welcome to the forums.

    You should for this problem set up an augmented system and apply row-operations.

    You could use MATLAB though and invert the matrix in terms an unknown number a and then check that you don't get an inconsistent system since a is in the RHS vector.

    Show us what augmented system have and row operations to get your reduced system
  4. May 19, 2012 #3


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    Homework Helper

    What Chiro said is true, but it's probably quicker to start by factorizing ## (a^2 - a - 2)z = a+1## into ## (a+1)(a-2)z = a+1 ##, and thinking about when that equation has zero, one, or many solutions.
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