Hi Professor Tao,
I am kinda confused by Q7 (a) and (b). For (a), I try to let x1, x2 be contined in V such that x1 can be written as y1 + y2; x2 can be written as z1 + z2, in which y1, z1 are contined in W1 and y2, z2 are contained in W2. I then proceed to prove the validity of the zero element, vector addition and scalar multiplication. However, I don't understand the difference between (a) and (b). Could you give me some hints at solving (b)? Thanks!
Best,
Doug