I was watching Professor Gilbert Strang's lecture on Linear Algebra, and in the video, he talks about when we can or cannot say that linear combinations of vectors span the entire region in that dimension.
He said that if we had nine vectors, each of dimension 9, and if the vectors were all random, then the answer is probably yes. But if it is the case that two of the nine vectors are the same, then they don't add anything new to the equation, and what we will get is probably an 8-dimensional plane.
I don't understand how this is the case.
Also, could someone explain what this means in terms of the number of solutions we will get?