Question

how many pivot columns must a 4x6 matrix have if its columns span R4

Answer 1

I believe it is 4 but can no give a good reason why

Answer 2

Yes, it only spans a much as it has unique rows and unique columns of.

Answer 3

Some proofs related to this:
http://www.math.northwestern.edu/~clark/285/handouts/col-basis.pdf

Not exactly it, but they talk about the column span.

Answer 4

thank you

Answer 5

np. have fun!