Please guys, this is due tomorrow and I'm really not sure what to do about it...Can I please get some help here?
I actually have 2 questions, both of which need answers and proofs. Also, if anyone has any ideas of places on the Internet that offer help for this type of stuff (I've tried many LA sites, but none help), they would be much appreciated.
If Q is the field of rationals, is Q(root 2) = {a+b(root 2) | a,b elements of Q} a (sub)field (of the real numbers)? Please prove.
AND
If Z_13 = F and W_F = span ((3,3), (5,5)) is V_F contained in W_F? Is W_F contained in V_F? Again, please prove.