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:



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



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





(x,y,z,w) = (-9,-38,-18,9)
 
Edwin