Q2. Let V = {x € R: x>0}, and define addition and scalar multiplication (over R) as

follows. For all x, y EV and te R,

xy=xy and tox= x.

The set V together with these operations forms a vector space over R, and you will prove

some parts of this!

(a) (i) What is the zero vector in this vector space?

(ii) If = 3 € V, what is -7?

(b) Show that axiom 6 (from the course notes) is satisfied by V with the above addition and

scalar multiplication. [You can check the other axioms if you want to convince yourself

that V is indeed a vector space over R, but you don't need to do the extra work.]

(c) Find a basis for V and compute dim(V).