Let $A\in \mathbb{F}^{m×n}$. The row rank of $A$ is the dimension of the row space of $A$.
Show that the row rank of $A=$ row rank of its RREF. Show that the row rank of $A$ is equal to rank of $A$.
Hello. Any suggestions, outlines, or hints for this one. I've been really messing it up. Thanks.
Hint: the row rank of $A$ is the number of linearly independent rows. When transforming $A$ into its reduced row echelon form, you add multiples of one row to another. Do these row operations affect the independence of the rows involved?