I have encountered the definition of a diagonal in a matrix in an echelon form like this.
$$ \left[ \begin{array}{ccccc} \mathbf{1} & \ast & \ast & \ast & \ast \\ 0 & \mathbf{1} & \ast & \ast & \ast \\ 0 & 0 & \mathbf{0} & 0 & 0 \\ 0 & 0 & 0 & \mathbf{0} & 0 \\ 0 & 0 & 0 & 0 & \mathbf{0} \\ \end{array} \right] $$
The pattern of a matrix in row echelon form is in the main diagonal of the matrix, the components (number) are only 1 or 0, and below the diagonal, every component (number) is 0. To the right side of the component with the value 1 in the diagonal, any number is allowed, to the right side of the component with the value 0 in the diagonal, only 0 is allowed.
But then I encounter this example which is very confused like this.
$$ \left[ \begin{array}{ccccc} \color{blue}{3} & 0 & \ast & \ast & \ast \\ 0 & 0 & \color{blue}{1} & 0 & \ast \\ 0 & 0 & 0 & \color{blue}{-4} & \ast \\ \hline 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ \end{array} \right] $$
Why in echelon form example, the number on the right side of 0 value in main diagonal can be a number which is difference from zero, is that conflict with the definition of echelon form?
And what is the pivot ?