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 Post subject: Linear Independence and bases helpPosted: Wed, 18 Feb 2009 08:46:36 UTC
 S.O.S. Newbie

Joined: Wed, 18 Feb 2009 08:43:57 UTC
Posts: 1
Hi:
I was reading over my linear algebra book, and trying to study for a midterm, but they didn't provide these conceptual answers in the back of the book.
So I was wondering if anyone could show me how the following three questions are done.

Thanks.

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 Post subject: Posted: Wed, 18 Feb 2009 17:19:17 UTC

Joined: Thu, 15 Feb 2007 06:35:15 UTC
Posts: 755
for 1 all you need to prove is that they are linearly independent, because if they are, then that means you have a linearly independent family with the same dimension as the base, and therefore it is also a base. To prove the linear independancy just try writing it out in summation form, it should be pretty cleare why..

i assume the "nullspace" means the kernel (all the elements that map to 0). Meaning the map is injective. Once again the trick to this one is writing them out in a summation and then using the linearity properties

3 you should be able to do on your own if you know what a basis is... just think addition and stick with easy identity-style matricies

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