I'm just having a small trouble understanding the difference ( occurred while I was doing exercise). 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?