krz

10-21-2007, 03:53 PM

Hey I'm doing a couple problems and can't figure one of them out. This one sounds very basic but I'm just bad at the abstract stuff.

i. Consider a space, P, whose each elements are diagonal matrix. Show that space P is a Vector Space

ii.What is the dimension of the above vector space P. Show a set of basis vector for P.

iii.(This question is not related to the above two parts.) Consider a vector space V whose dimension is 3, dim(V)=3. Suppose you are given 20 vectors, , from this space V such that any three vector are linearly independent. How may set of basis vectors can be formed for the set.

specifically i. I think I can figure out the other ones.

i. Consider a space, P, whose each elements are diagonal matrix. Show that space P is a Vector Space

ii.What is the dimension of the above vector space P. Show a set of basis vector for P.

iii.(This question is not related to the above two parts.) Consider a vector space V whose dimension is 3, dim(V)=3. Suppose you are given 20 vectors, , from this space V such that any three vector are linearly independent. How may set of basis vectors can be formed for the set.

specifically i. I think I can figure out the other ones.