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)?

$a)$ For the vectors to be independent, the relationship $\lambda_{1}a_1+\lambda_{2}a_2=0 $
must yield $\lambda_1=\lambda_2=0$.
You can verify that this is the case here.
$b)$ You have two linearly independent vectors. This means that any $v \in V$, where $V$ is the vector space created by $a_1, a_2$ can be written as their linear combination. That is, $v=\kappa_1a_1+\kappa_2a_2$.
Now all you have to do is (re)check the definitions found on your course notes/book to see if it holds true.. Same for $c)$.
