Linear Independence and bases help

[wm1734]

Hi:
I was reading over my linear algebra book, and trying to study for a midterm, but they didn't provide these conceptual answers in the back of the book.
So I was wondering if anyone could show me how the following three questions are done.

Thanks.

 

[daon]

If {v1, v2} forms a basis for V, then {v1, cv1 + v2} does also. Wet w be any vector in V, using our basis, so that w= x(v1)+y(v2). Then we can write this using vectors from {v1, cv1+v2}: v=(x-yc)(v1)+(y)(cv1+v2)=w.