Ok, so a set of vectors is linearly independent if each pair of vectors in it are linearly independent i.e. they aren't scalar multiples of each other.
Another way to say this (and useful from the point of view of this question) is that a set of vectors
v1,…,vn is linearly independent if the only linear combination
λ1v1+⋯+λnvn of them equal to zero is the trivial one i.e. the one where each of the
λi is zero.
If a set of vectors is not linearly dependent, it is called linearly dependent. A linear dependence between a set of vectors just means writing one vector as a linear combination of the others i.e. it is a nontrivial solution to the equation:
λ1v1+⋯+λnvn=0.
So, you want to find linear dependencies and remove all vectors that are linearly dependent on the remaining ones until you are left only with a linearly independent set whose span as the same as the original.
So what is the span of a set of vectors?
How would you go about finding solutions to the above equation? (and be precise here - don't just say "write a matrix" - be specific as to how it is equivalent to the above equation)
You are still trying to jump the gun, sure you are starting to understand what any of this has to do with matrices but if you persevere a tiny bit more, you can say precisely which matrix we should look at and why. Remember that jumping straight to the matrix without having anything other than a vague memory of seeing them in this scenario before was why you were stuck.