I'm finding it difficult to grasp the concept of rank (more specifically, of bases). First of all, what excactly is a basis? The text book definition doesn't suffice. What is "column space" (colA) and "row space" (rowA)? If I am given a matrix A and told to find the bases for rowA and colA, how do i go about doing this? At first i thought of doing the following: convert A --> U (row echelon form); the non-zero rows is the basis for rowA and the columns with non-zero leading values correspond to the columns of A which are the bases for colA. Am i right? And if i am, why am i? I really don't understand the concept. Thank you.