Morning/night I have a few general questions about basis and vector spaces, I'll be very very grateful if you could point me into direction
1) If I have a M2x3(R) vector space, how do I find the basis? I found span, but it's a matrix, how do I check if two matrices are independent?
2) If I'm given a vector space that is already a span, do I do the same thing? Just check if it's also independent? What if it's not - Do I remove the vectors that are dependent, and if n is then less than the field - I complete it with vectors from the standard basis?
3) How do I check if
M = {p(x) element of R4[x] | p(-1)=p(1)=p(0)}
is a vector space?
4) I need to prove that for V, U vector spaces of R^n, if dimV=dimU=n-1 then U+V=R^n. How do I start? I'm not sure I understand the question; I need to find U,V so that their dim is say 2, but their union is basis of R^3?
Have a great day