Dimension of vector space and span I have the following problem

a) I say that the vectors are linearly independent because they are not scalar multiples of each other.
b) This one I'm struggling with. How do I find the dimension of the vector space? Is it 3 dimension due to the fact that the vectors only have 3 coordinates? Is it so simple?
c) I'm not sure what to say here. I don't think it belongs belongs to the span. If this is true, can it be explained by the same reasoning as in a)?

Answering each of your questions:
a) True, they are linearly independent (it's easily seen that they're not schalar multiples of each other). You can see this from noticing that in the second component, $a_1$ has $-1$ and $a_2$ has $1$, but the other components aren't the same with opposite symbols.
b) Since they are linearly independent, then the vector space generated by both vectors (or how it's written: $\langle a_a,a_2\rangle$) is of dimension $2$ (it would have been dimension $1$ if they were linearly dependent).
c) Since $a_1$ is not a schalar multiple of $a_2$ (because they are linearly independent), you conclude that $a\notin \langle a_2\rangle$.
As you see, all of your questions have to do with the same important question: are those vectors linealy independent? The answer to that is yes, and the following statements are concluded from there.
