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!

Linear Algebra Solution Set Question

  1. Sep 25, 2008 #1
    1. The problem statement, all variables and given/known data
    Find all solutions of a for which the resulting linear system has (a) no solution, (b) a unique solution, (c) infinetly many solutions.


    2. Relevant equations

    ...Row reduction

    3. The attempt at a solution

    I solved the augmented matrix and got z=a-5/[(a-2)(a-3)], then got x and y in terms of z. I solved the homogeneous and only got the trivial solution regardless of a's value. I'm thinking that the system has no solution when a=2 or a=3, and has a unique solution when a equals any other real number. Is this correct?
  2. jcsd
  3. Sep 25, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, that is correct. The only way you could have "infinitely many solutions" would be if you arrived at something like "z= (a-2)/[(a-2)(a-3)]". In that case, any value of z would satisfy (2-2)(2-3)z= (2-2) so there would be infinitely many solutions for a= 2.. (I haven't checked your calculations. I am assuming you did not cancel something like (a-b)/(a-b) in your solution.)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?