Results 1 to 2 of 2

Math Help - Linear Independence and Basis

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    6

    Exclamation Linear Independence and Basis

    Thank you so much for taking time to read this. I'm in deep trouble so any help will be very appreciated.

    (1) Prove that a set S of vectors is linearly independent iff each finite subset of S is linearly independent.

    (2) let f,g in F(R,R) be the functions defined by f(t)= e^(rt) and g(t)= e^(st) where r does not equal s. Prove that f and g are linearly independent in F(R,R).

    (3) Let V be a vector space having dimension n, and let S be a subset of V that generates V.
    a. Prove that there is a subset of S that is a basis for V. (You cannot assume that S is finite)
    b. Prove that S contains at least n vectors.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member tukeywilliams's Avatar
    Joined
    Mar 2007
    Posts
    307
    For (2) you could take the Wronskian and show that it is not equaled to  0 .

     \det \begin{bmatrix} e^{rt} & e^{st} \\ re^{rt} & se^{st} \end{bmatrix} = se^{rt+st}- re^{rt+st} \neq 0 (assuming that  s \neq r ) which implies that they are linearly independent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Algebra: Linear Independence question
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 3rd 2011, 05:28 AM
  2. Linear independence
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 24th 2010, 11:58 AM
  3. Linear Independence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 5th 2009, 03:17 AM
  4. Linear Independence in linear transformations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 17th 2009, 04:22 PM
  5. Linear Transformations and Linear Independence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 6th 2008, 07:36 PM

Search Tags


/mathhelpforum @mathhelpforum