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!

Linear Independence. express each vector as a lin. combo

  1. Jan 30, 2013 #1
    V1 = (1,2,3,4) V2 = (0,1,0,-1) V3 = (1,3,3,3)

    a) I already expressed them a linearly dependent set in R4

    b) Express each vector in part (a) as a linear combination of the other two

    linear combo is just {c1v1 + c2v2.....cnvn} right? But I don't get where to start to prove this
     
  2. jcsd
  3. Jan 30, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    There is nothing to prove; that is just a *definition* of "linear combination". You are being asked to represent v1 as a linear combination of v2, v3, and so forth. To start: just write things down in detail: figure out what are the components of c2v2 + c3v3 for constants c2 and c3. How can that combination be equal to v1?
     
  4. Jan 31, 2013 #3
    so are you saying take v1 = c2 (v2) + c3 (v3) using the constants that I found through proving that they are linearly dependent?
     
  5. Jan 31, 2013 #4

    Mark44

    Staff: Mentor

    What Ray is saying has three parts.
    1) Find constants c2 and c3 for which v1 = c2v2 + c3v3
    2) Find constants c1 and c3 for which v2 = c1v1 + c3v3
    3) Find constants c1 and c2 for which v3 = c1v1 + c2v2
     
  6. Jan 31, 2013 #5

    Mark44

    Staff: Mentor

    BTW, when you post a question, do not throw away the three parts of the template. They are there for a reason.
     
  7. Jan 31, 2013 #6
    Thx. I will leave the template. So im left with 3 different equations in the form of vn = cx(vx) + cy(vy) as my final answer?
     
  8. Jan 31, 2013 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    That would be one way of doing it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear Independence. express each vector as a lin. combo
Loading...