Results 1 to 2 of 2

Math Help - question about procedure in determining if vectors form a basis

  1. #1
    Senior Member
    Joined
    Jun 2009
    Posts
    251

    question about procedure in determining if vectors form a basis

    If I'm given a set of vectors and asked to determine whether they form a basis of a certain subspace, I check to see if they are linearally independent and check to see if they span the subspace. So isn't that doing the same work twice? What I mean is that to check to see if they are linearally independent I'd put them into rref and if there's anything asside from 1s and 0s they are linearally dependent. For them to span the subspace they I would put the vectors in rref and basically if they don't form the identitity matrix they don't span the subspace. So putting it simply, isn't it enough to take the matrix, put it in rref, and if it doesn't give the identity matrix (unless there's extra rows of 0s on the bottom) then it's doesn't form a basis?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298
    A basis has three properties:
    a) the vectors are independent
    b) the vectors span the space
    c) the number of vectors in the set is equal to the dimension of the space.

    Further, any two of those is sufficient to prove the third.

    If you know the dimension of the subspace and can see that the number of vectors in the given set is equal to that, then you only need show that they are independent or that they span the space.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: June 30th 2011, 08:05 PM
  2. [SOLVED] Finding/determining equidistant point between vectors.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 13th 2011, 05:42 PM
  3. Replies: 1
    Last Post: June 6th 2010, 09:29 AM
  4. Vectors, Component Form and Geometric Form
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 15th 2009, 12:41 AM
  5. [SOLVED] [SOLVED] A C# /C++ Procedure/Function to be converted to mathematical form
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: August 16th 2006, 03:28 PM

Search Tags


/mathhelpforum @mathhelpforum