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Linear Alg: Find all values of a and determine all solutions

  1. Jan 28, 2015 #1
    1. The problem statement, all variables and given/known data

    x - 2y + z = 0
    x + ay - 3z = 0
    -x + 6y - 5z = 0

    2. Relevant equations
    3. The attempt at a solution


    i've got it reduced all the way down to
    1 0 0 0
    0 1 -1 0
    0 0 -1a+3 0

    I could show more of the steps if needed, but im just wondering what I can do to reduce the matrix further, or how i could get solutions from what i have so far
     
  2. jcsd
  3. Jan 28, 2015 #2

    O_o

    User Avatar

    I think your reduced form is off.

    I get

    1 0 -1
    0 a-2 0
    0 1 -1


    If you want to find the solutions then you need to figure out what this matrix is telling you. Start with rows 1 and 3. What do they tell you about the relationship between x, y and z? If you can figure out those then we can move onto the second row which is slightly different.
     
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