here question:

2. (a) Show that the set 1C2 is a complex vector space with respect to the vector addition and scalar multiplication defined by II + Ell __ I1+y1+1 a $1 ._ 031+1 Is 29': ._ Ia+ya+1 3' lg "_ oz2+cr1 ' Are the vectors (g) and (g) linearlyr independent in this vector space? (h) Let X be an arbitrary set. Show that the power set 'P{X} is a vector space over the trivial field {I}? 1} with respect to the vector addition and scalar multiplication defined by Y1 +1r'2 .-= 11.513 and HY .'= EL IF := Y. [Note: The power set \"PDQ is the set of all subsets of X. The symmetric difference of two sets A and B is AB :2 [Au B} l. [Am 3).] [c] Show that (JR, +1 forms a finitedimensional vector space over {R1+1.} but an infinite dirnensional vector space over (Q, +,. .}