well, i'll do the first one for you and you do the second one..

i) suppose and are linearly dependent. then there exists a nonzero scalar such that

then,

this means that which contradicts the fact that { } is a basis for .

hence, and must be linearly independent.

ii) Let . since { } is a basis for , we have for some scalars and in . In particular, let and where and are scalars in . Hence, . Thus, implies since we have written as a linear combination of . Clearly, . Therefore, .