I've been given a question that asks me to determine whether a given vector is in the span of a set of vectors. I understand the concept of span and how to tell whether a vector is in the span, but there is one small thing I'm not quite certain of.
I know that to find out whether a vector is in the span, you row reduce the matrix containing the vectors in the set with the vector you're trying to test in the last column. If the row reduced outcome is consistent, then the vector is in the span. Of course I could have read the chapter wrong and not been doing it right, so if that's the case, please let me know.
My question is, if your outcome is a perfectly row reduced matrix, with 4 pivot columns in a 4x4 matrix for example, does this still count as an inconsistent system because of the last row?
Hopefully I explained that right, but let me know if I didn't. Thanks in advance for the help!