1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Mark44

    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

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

    radou

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook