Is the last line of the row ladder matrix all zero? It's written in the book, but I don't know what's going on. Is it a convention? It's not stated in the definition,

Is the last line of the row ladder matrix all zero? It's written in the book, but I don't know what's going on. Is it a convention? It's not stated in the definition,

Row ladder matrix is a matrix in which the non-zero first element of each non-zero row appears to the right of the non-zero first element of the previous row, and no non-zero row appears below the zero row
For example:
1 3 0 1
0 2 1 0
0 0 0 1

What is a row ladder matrix

This is the definition. Pay attention to the shape drawn by the red line

How to judge whether a matrix is a ladder matrix?

See if the column number of the first non-zero number in each row is decreasing. If yes, it is a row ladder matrix, otherwise it is not