Question

Can somebody give me an intuitive idea of why the row-rank = col-rank?

Answer 1

Because reduction to reduced row echelon form produces r pivots, r independent rows or columns

Answer 2

Im not sure what pivots are but I know the rank of a matrix is the # of rows with a leading 1s in RREF

Answer 3

Those 1s are pivots and those rows are called pivot rows, the intuition comes from the RREF process itself, ie. there is no way to get a zero vector by a linear combination of those rows other than the combination where all coefficients are zero, making those rows or columns independent

Answer 4

Ah! that makes a lot of sense :) Thank you!