I'm not sure whether you understand clearly what linear independence is about. I assume you know the formal definition. The "basic idea" is that none of these three (or perhaps more, in another case) vectors can be constructed by adding together any multiples of the other two (or perhaps more). If you think of these vectors as arrows or directed line segments from the origin, it means that there is no plane that contains all three. Two vectors in a plane can be used to construct another vector in the same plane, but not any vector that isn't in that plane. Is that clear?

In this case, B contains two vectors of three elements. The only way two vectors (of however many elements) can be linearly dependent is if each is a multiple of the other. Is that the case here? No. You should be able to see that 1:2 is not the same as 4:7.

Now if vector u can be made by combining v1 and v2, it is in the span of B. The way to find out is to construct a 3x3 matrix where the columns are v1, v2 and u and row-reduce them. If they come out with a row of zeroes at the bottom, then u is in the span of B.

See the pdf.

Let me know if I lost you anywhere.

If you got this, then we can get to work on the other questions.