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!

Homework Help: 2 vector proofs

  1. Aug 15, 2009 #1
    Suppose S is a set of n linearly independet in the n-dimensional vectorspace V. Prove that S is a basis for V.

    My try at this proof is:
    For S to be a basis for V it has to span V and the vectors in S needs to be linearly independent. But they have allreade sad that the vectors in S are linearly independent, so we only needs to show that it spans V.

    But since V is n-dimensional it means that n linearly independent vectors in V span it, hence since S has n linearly independent vectors and is in V, S is a basis for V? Is this right?

    Suppose that S is a set if n vectors that span the n-dimensional vector space V. Prove that S is a basis for V.

    Now we need to show that the vectors in S is lineraly independent, right? But since n is n-dimensional it means that n lineraly independent vectors span it, since S is a set of vectors that spans V and S has n vectors, S is lineraly independent? Have I proved this one right?
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted