The following matrix is obtained from a system of 
equations
1 0  6  5
0 1 -4  3
0 0  2 -6 The solution to the system is 
My answer is no solution after using Excel. 
thanks for looking at this problem.

No, there is a solution. 

[1 0  6  5]
[0 1 -4  3]
[0 0  2 -6]

is the matrix for the system

1x + 0y + 6z =  5
0x + 1y - 4z =  3
0x + 0y + 2z = -6 

or

 x      + 6z =  5
      y - 4z =  3
          2z = -6 


Solve the bottom equation for z
     
          2z = -6
           z = -3

Substitute -3 for z in the middle equation

      y - 4z = 3
   y - 4(-3) = 3 
      y + 12 = 3
           y = -9

Substitute in the first equation:

      x + 6z =  5
   x + 6(-3) = 5
      x - 18 = 5
           x = 23

The solution is (x, y, z) = (23, -9, -3) 

Edwin