Question 732096
<pre>
  x - 2y + 3z      =  13
       y -  z +  w = -11
-3x + 3y - 2z + 5w =  -6
      2y - 3z +  w = -13

 1x - 2y + 3z + 0w =  13
 0x + 1y - 1z + 1w = -11
-3x + 3y - 2z + 5w =  -6
 0x + 2y - 3z + 1w = -13


The cefficient matrix is thi 4x4 matrix:

{{{(matrix(4,4,

 1, -2,  3,  0, 
 0,  1, -1,  1, 
-3,  3, -2,  5, 
 0,  2, -3,  1))}}}

Find its inverse using a TI-83 or better calculator.
That's this 4x4 matrix

{{{(matrix(4,4,

 1/4, 5/4,  -1/4,  0, 
 -3/2,  11/2, -1/2,  -3, 
-3/4,  13/4, -1/4,  -2, 
 3/4,  -5/4, 1/4,  1))}}}

Multiply that by the 4x1 column vector or matrix
from the numbers on the right of the system:

{{{(matrix(4,1,
13,-11,-6,-13))}}}

{{{(matrix(4,4,

 1/4, 5/4,  -1/4,  0, 
 -3/2,  11/2, -1/2,  -3, 
-3/4,  13/4, -1/4,  -2, 
 3/4,  -5/4, 1/4,  1))(matrix(4,1,
13,-11,-6,-13))}}}{{{""=""}}}{{{(matrix(4,1,
-9,-38,-18,9))}}}{{{""=""}}}

(x,y,z,w) = (-9,-38,-18,9)
 
Edwin</pre>