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Homework Help: Finding System Solutions of the system Ax=0; A being a matrix

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data

    Find all solutions of the system Ax=0
    where A = the 3x3 matrix

    [1 3 2]
    [2 6 9]
    [2 8 8]

    2. Relevant equations

    not really sure what equations to include

    3. The attempt at a solution

    wasnt positive how to go about answering this question because im not sure what its asking for...

    i turned "x" into a 3x1 matrix consisting of x1, x2 and x3 and tried to solve the system of equations...

    1x1 + 3x2 + 2x3 = 0
    2x1 + 6x2 + 9x3 = 0
    2x1 + 8x2 + 9x3 = 0

    after trying to solve this as a linear system of equations problem, i ended getting that each value (x1, x2, x3) was equal to 0... is this anywhere close to a correct approach to this problem? Thanks for any help you have to offer :smile:
  2. jcsd
  3. Jan 28, 2010 #2
    Yes, since this matrix is indeed invertible.
  4. Jan 28, 2010 #3


    Staff: Mentor

    Do you know about row operations for reducing a matrix? If you do, using them to reduce your matrix would be simpler than solving three equations in three unknowns.
  5. Jan 28, 2010 #4
    My class learned about row operations today but I didn't think to apply them because I began this problem yesterday...

    Thanks for your advice :biggrin:
  6. Jan 29, 2010 #5


    User Avatar
    Science Advisor

    If A is invertible, then the only solution to Ax= 0 is x= 0.
  7. Jan 29, 2010 #6


    User Avatar
    Homework Helper

    This is a linear system of equation which is equivalent to the matrix representation of the problem. And yes, your solution is correct, as far as I checked.
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