rank of a matrix by linearly independent rows

Question

In the book it says,the rank of a matrix in echelon form is the maximum number of linearly independent rows and that is equal to the number of non zero rows in the matrix,

I am aware of echelon form of a matrix but have no ideas how to get the maximum number of linearly independent rows and how that is equal to the number of non zero rows,

I will be grateful if anyone can help me undeestand it by giving simple examples,

thanks.

Answer 1

$\begin{bmatrix} 1& 1\\2&2\end{bmatrix}$. How many rows do you see in the matrix ? 2 right? But is the second row really of any use? Its just $2$ times the first row, i.e., it depends on some other row for its formation. Just to show it mathematically, you do $RREF$ to get
$\begin{bmatrix} 1& 1\\0&0\end{bmatrix}$.