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 Algebra Subspaces Basis

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    a) If U and W are subspaces of R^3, show that it is possible to find a basis B for R^3 such that one subset of B is a basis for U and another subset of B (possibly overlapping) is a basis for W.

    b) If U and W are subspaces of a finite-dimensional vector space V, show that it is possible to find a basis for V such that one subset of that basis is a basis for U and another subset of that basis (possibly overlapping) is a basis for W.


    2. Relevant equations

    none really

    3. The attempt at a solution

    B = ( v_1, v_2, v_3 ), such that these vectors are a basis for V.

    Then:

    V = t_1*v_1 + t_2*v_2 + t_3*v_3

    ...stuck here
     
  2. jcsd
  3. Oct 5, 2011 #2
    help please!!!
     
  4. Oct 5, 2011 #3
    Please guys
     
  5. Oct 5, 2011 #4

    Evo

    User Avatar

    Staff: Mentor

    People will help if they wish. They probably will not help you since you keep bumping your thread every few minutes, which is against the rules.
     
  6. Oct 5, 2011 #5
    V = (v_1, v_2, v_3)
    U = ??? it never told us

    Please can someone help.
     
  7. Oct 5, 2011 #6
    Guys please, I'm begging you
     
  8. Oct 5, 2011 #7

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Start off by finding a basis for [itex]U\cap W[/itex].
     
  9. Oct 5, 2011 #8
    U = (v_1, v_2)
    W = (v_2, v_3)

    U∩W = (v_2)
     
  10. Oct 5, 2011 #9
    please i need to this quickly
     
  11. Oct 5, 2011 #10

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    No, what makes you think that U and W are two-dimensional?? U and W can be anything!!

    First construct a basis for [itex]U\cap W[/itex], then extend this basis to a basis of U and extend it to a basis of W.


    Messages like this actually incline people to help you less. Just so you know.
     
  12. Oct 5, 2011 #11

    Evo

    User Avatar

    Staff: Mentor

    24 hour time out due to ignoring the rules, ignoring the warning and continuing to bump.
     
  13. Oct 6, 2011 #12

    berkeman

    User Avatar

    Staff: Mentor

    Do you need it quickly because it is part of a midterm exam?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear Algebra Subspaces Basis
Loading...