1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: True/False Question on Linear Combos

  1. Oct 1, 2012 #1
    1. The problem statement, all variables and given/known data
    If the system Ax=b has two known solutions, x1 and x2, true or false that another solution exists. If it does, find another solution.

    2. Relevant equations

    3. The attempt at a solution
    I think it's true. But after that, I don't know.

    I'm really lost, but I think I remember learning that given two solutions, any linear combination of the two is also a solution. Does that mean that x1+x2 is a solution?

    I'm worried that that is actually a solution to Ax=2b, though.
  2. jcsd
  3. Oct 1, 2012 #2
    Perhaps that is only true for homogeneous equations, now that I think about it.

    Would nonhomogeneous equations require some sort of weighted average linear combination?
  4. Oct 1, 2012 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Is it true that (1/2)Ax = A((1/2)x) ?
  5. Oct 1, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Is it given b is not the zero vector? Think about uniqueness, rank, and free variables.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook