Echelon Form

Echelon forms the products of matrix elimination, and they are useful for revealing fundamental properties of the matrix, such as:
 * Rank of matrix
 * Basic columns of matrix
 * The relationships between the columns of the matrix (see p49-50 and p135-136 in )

Row echelon form
$$ \begin{bmatrix} \circledast & \ast & \ast & \ast & \ast \\ 0 &\circledast &\ast &\ast& \ast \\ 0&0&0&\circledast & \ast \\ 0&0&0&0&0& \end{bmatrix} $$