Here's the question I'm trying to answer:
Suppose a 6 x 8 matrix A has four pivot columns. What is dim Nul A? Is Col A = R4? Why or why not?
I know that dim Nul A = 4 because there are 4 columns that are not pivot columns. But I'm unsure about the column space. I know that the four pivot columns consisting of Col A are linearly independent, but the column vectors of A exist in R6, not R4, because A is 6 x 8. Is having 4 linearly independent column vectors enough to say that they span R4, or is this statement untrue if the vectors are not in R4 to begin with?
I'd appreciate any insight!