Results 1 to 2 of 2

Math Help - Linear dependent vectors

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    124

    Linear dependent vectors

    Consider a linear transformation T from R^n to R^p and some linearly dependent vectors v1, v2, ..., vm in R^n. Are the vectors T(v1), T(v2), ..., T(vm) necessarily linearly dependent? How can you tell?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Quote Originally Posted by noles2188 View Post
    Consider a linear transformation T from R^n to R^p and some linearly dependent vectors v1, v2, ..., vm in R^n. Are the vectors T(v1), T(v2), ..., T(vm) necessarily linearly dependent? How can you tell?
    Yes. Let v_m= a_1v_1 + ...+a_{m-1}v_{m-1} then T(v_m)=a_1T(v_1)+...+a_{m-1}T(v_{m-1}) which shows T(v_i) are linerly dependent
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linearly dependent vectors and spans
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: August 2nd 2010, 04:57 PM
  2. show that the vectors are linearly dependent
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 29th 2009, 03:36 PM
  3. Prove that vectors ... are linearly dependent ...
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 21st 2009, 09:40 PM
  4. Vectors Linear Dependent?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 23rd 2008, 03:20 AM
  5. Dependent/Combination Vectors
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 27th 2008, 08:54 PM

Search Tags


/mathhelpforum @mathhelpforum