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A basis is defined as

1)linearly independent

2)spans the space it is found in.

Here is where I get confused:

To determine whether or not a set spans a vector space, I was taught to find its determinant and if det|A|=/= 0 then it spans the space.

I was also taught that if det|a|=/=0 then it isn't coplanar and therefore it is linearly independent ( can also just solve to see if trivial sol'n...)

But then if both det|a=/= it means that it spans and is linearly independent. Therefore, in my head, it comes with the idea that "spans is related to independence"

Anybody got a good way to differentiate both?