Question 824854
Since algebra.com doesn't do matrices very well, I will just show the rectangular array of numbers.<br>
<pre>
x+y+z=9
3x-y+z=-1
-2x+2y-3z=-2
translates into the augmented matrix:
    1    1    1    9
    3   -1    1   -1
   -2    2   -3   -2
Added -3 times row 1 to row 2.
     1     1     1     9
     0    -4    -2   -28
    -2     2    -3    -2
Added 2 times row 1 to row 3.
     1     1     1     9
     0    -4    -2   -28
     0     4    -1    16
Replaced row 2 with -1/4 times row 2.
     1     1     1     9
     0     1   1/2     7
     0     4    -1    16
Added -1 times row 2 to row 1.
     1     0   1/2     2
     0     1   1/2     7
     0     4    -1    16
Added -4 times row 2 to row 3.
     1     0   1/2     2
     0     1   1/2     7
     0     0    -3   -12
Replaced row 3 with -1/3 times row 3.
     1     0   1/2     2
     0     1   1/2     7
     0     0     1     4
Added -1/2 times row 3 to row 1.
     1     0     0     0
     0     1   1/2     7
     0     0     1     4
Added -1/2 times row 3 to row 2.
   1   0   0   0
   0   1   0   5
   0   0   1   4
which translates back into:
x = 0
y = 5
z = 4