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!

Express as a linear combination

  1. Mar 26, 2008 #1
    1. The problem statement, all variables and given/known data
    The vectors v1= [1, -3], v2= [2, -8], v3= [ -3, 7] span R2 but do not form a basis. Find 2 different ways to express [1, 1] as a linear combination of v1, v2, v3.

    3. The attempt at a solution

    Since it states that the set is not a basis, then v3=v1+v2. I solved the system v1+v2=[1,1] and got 5v1-2v2=[1,1]. The second answer the book gives is 10v1-3v2+v3. How did they get the second answer?
  2. jcsd
  3. Mar 26, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    If you solve c1*v1+c2*v2=[1,1] you get a unique solution since [v1,v2] are a basis. To get the second answer you solve c1*v1+c2*v2+c3*v3=[1,1]. Since [v1,v2,v3] are linearly dependent, and hence are not a basis, you get an infinite number of solutions. The books answer is only one of them.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?