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-question.

  1. Oct 2, 2005 #1
    Linear Algebra-question. HELP!!


    Let [itex]L: R^3 \rightarrow R^4[/itex] be a linear transformation that satisfies:
    [itex]L(e_1) = (2,1,0,1)^T = u[/itex]
    [itex]L(e_2) = (0,3,3,4)^T = v[/itex]
    [itex]L(e_3) = (2,-5,-6,-7)^T = w[/itex].

    Determine a base for [itex]Range(L)[/itex].


    Is the base [itex]\{u,v\}[/itex] since [itex]w = u-2v[/itex]? Is it really that simple? :blushing:
    Last edited: Oct 2, 2005
  2. jcsd
  3. Oct 2, 2005 #2
    Help anyone??
    Last edited: Oct 2, 2005
  4. Oct 2, 2005 #3
    :cry: :cry:
  5. Oct 2, 2005 #4

    there's a theorem saying that the basis of the range of a transformation is given by the set determined by the transformations of the vectors comprising the basis of the domain of the transformation.

    and you used this and noted that the third vector is a linear combination of the other two...

    so... yeah, you found the basis for the range of the transformation.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear Algebra-question.