How can I determine if one set of vectors has the same span as another set using ONLY the Elimination Theorem?

Question

In my Linear Algebra course textbook, we are asked to determine which subsets have the same span as the original set using only the Elimination Theorem, as can be seen in the link to the screenshot. (BTW, I've looked up and down the Internet for more lessons on using the Elimination Theorem for multiple types of problems, but I have not found anything yet, not even anything explicitly labeled "Elimination Theorem", which makes me think it could go by a different term.) I am aware that if a set has vectors that are linearly dependent, you can "eliminate" those vectors until you get down to a certain set of vectors which can no longer be eliminated, and thus, you've arrived at a set of vectors which are linearly INDEPENDENT. I've worked on problems that give us a set of vectors with specific vector components with no issue at all. However, in this problem, they do not provide specific vector components, and my issue is that I don't know how to approach this problem. According to the textbook, the answer is: a, b, and d. Any help would be greatly appreciated.

Elimination Theorem

Problem 7

Answer 1

I get $a,b$ and $d$.

For instance $a$ does because $v_3$ can be eliminated, as it is in the span of $v_1$ and $v_2$.

$b$ does because we can eliminate one of $v_1,v_2$ and $v_3$... and one of $v_4$ and $v_5$.