I posted a question, which I have attempted all except for c. Could someone tell me if I did the question correctly? And how do I begin (c). Thanks, there is a PDF file attached.

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- February 11th 2010, 06:17 PMmillerstSubspace, Basis
I posted a question, which I have attempted all except for c. Could someone tell me if I did the question correctly? And how do I begin (c). Thanks, there is a PDF file attached.

- February 11th 2010, 08:07 PMNonCommAlg
in part (a) you have a couple of mistakes: in proving that W is closed under addition that should be changed to also is not in it's in your base field.

finally in order to show that a non-empty set is a subspace**you do not need**to prove that it contains unfortunately some instructors give this wrong idea to some students.

for part (b), the basis you found is wrong! you should at least see that none of the elements of the set that you think is a basis basically belongs to anyway, a basis of

has only one element. for example

for part (c) first see that an matrix with real (or complex) entries, is antisymmetric iff for all and for all can you

see the general form of ? if not, try to do it for n = 3 first. now it should be easy to show that a basis for antisymmetric matrices has elements. what are they? - February 11th 2010, 08:12 PMmillerst
So would it be correct to say that a = 0, therefore the set contains {0}. ?

- February 11th 2010, 08:14 PMNonCommAlg
- February 11th 2010, 08:17 PMmillerst
Then how exactly do you prove it contains a zero vector?

- February 11th 2010, 08:21 PMNonCommAlg
- February 12th 2010, 05:31 AMHallsofIvy
The reason why we often

**do**prove that the 0 vector is in the set is simply to prove it is**non-empty**- and 0 is typically easiest to work with. Here, you are asked to show that the set of anti-symmetric 2 by 2 matrices is a subspace and I would disagree with millerst- you are NOT given that it is non-empty, you need to show that. Of course, you could do that as well by showing that is in the set as by showing that is in the set.