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: Linear Algebra: linear equations

  1. Sep 14, 2009 #1
    Show that if u and v are solutions of the linear system Ax = b, then w = 1/4 u + 3/4 v is also a solution of Ax = b.
  2. jcsd
  3. Sep 14, 2009 #2
    Just plug it in and use the fact that matrix multiplication is linear.
  4. Sep 14, 2009 #3
    Plug what? where?

    Ax=b, then b=uv ? and uv=w? uv = 1/4u + 3/4v?
  5. Sep 14, 2009 #4


    User Avatar
    Science Advisor

    You want to show that w "is also a solution of Ax= b".

    So "plug" w in for x: Aw= what? Use the fact that w= (1/4)u+ (3/4)v and that A is a linear transformation.
  6. Sep 14, 2009 #5


    User Avatar
    Science Advisor
    Homework Helper

    Amy-Lee, forget x …

    you know that Au = b and Av = b,

    so just carry on from there. :wink:
  7. Sep 15, 2009 #6
    thanks TT, I will try that
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook