1 * x 1+0 * x2- 1 * x3- 1 * x4 = 1
0 * x 1+ 1 * x2+ 1 * x3+0 * x4 = 0
The third one is the same as the fourth one: 0*x 1+0*x2+0*x3+0*x4=0. It can be seen that only two equations are meaningful, so only two unknowns can be solved, and the remaining two can be taken at will. As for why it is the third and fourth unknowns, it depends on the specific equation. Simply put, the form of the above matrix means that x3 and x4 are free variables. Finally, the matrix ladder is simplified. If you look at which column is the first non-zero number (usually 1) in each row, then the variable corresponding to this column is not free variables. If the second row of the above matrix is changed to 0 0 1 1 00, then x3 is not free variables, and x2 is free variables.