This matrix is in "row echelon" form because each
row's left-most non-zero element is 1 and they
move to the right as we go down the matrix.  So the
matrix is an abbreviation for this system:


Removing all the 1 coefficients and the 0 terms:


We use "back substitution".

The bottom, fourth, equation is already solved for z,

so we substitute -2 for z in the third equation:













Now we substitute 3 for y and -2 for z in the
second equation:








Finally we substitute 2 for x, 3 for y 
and -2 for z in the first equation:






Solution (w,x,y,z) = (1,2,3,-2)

Edwin