The problem is attached. I'm having problems with parts a and c, well maybe not part a (probably just need to check if I did this part right. I'm just not sure if I'm wording part a right. Anyways for part a I must prove it's a subspace so I must satisfy 3 conditions: 1) 0 is in S 2) if U and V are in S, then U+V must be in S 3) if V is in S, then fV is in S for some scalar f. for 1) By inspection if a=b=c=0 then 0 is in S for 2) if U is of the form: a1-b1 a1 b1+c1 a1-c1 and V is of the form: a2-b2 a2 b2+c2 a2-c2 then U+V= a1+a2-b1-b2 a1+a2 b1+b2+c1+c2 a1+a2-c1-c2 Thus U+V is in S. <<< Can I say this? for 3) fV= f(a2-b2) f(a2) f(b2+c2) f(a2-c2) Thus fV is in S. <<< Can I say this? For part c, I don't even know where to begin. Can someone give me a hint?