I have several conceptual questions that have been confusing me for a while in linear algebra.
Let A be a 3 by 5 matrix with full rank rows. A is now simplified to Echelon form U and further simplified to row reduced form R. The question is
A) are the column spaces of U, R, and A all equal? Why or why not? (it is trivial to mention their dimensions' equality)
B) are the row spaces of U, R, and A all equal? Why or why not?
Thanks in advance.