Nevermind, I used my above example (1, 1) and (1,-1) for the second question and figured it out!
(1, -1) is a part of the subspace, and so is (1, 1), but their sum is not (2,0) (i.e. 2^2 =/= 0^2)
You check to see if there's a counterexample and/or if it's closed under addition/multiplication. Problem is my book has given no examples of something like these, and my professor went over it the day I was out of class so I have no idea how to work it out.
Edit:
Okay, I've figured out the...
Homework Statement
Determine whether the following sets form subspaces of R2:
{ (X1, X2) | |X1| = |X2| }
{ (X1, X2) | (X1)^2 = (X2)^2 }
Homework Equations
The Attempt at a Solution
I'm clueless. I've been trying to figure it out for a good thirty minutes on both of them, but I'm...