using Gauss and jordan find the solution to the system?

Question

3x-6y+9z=0
4x-6y+8z=-4
-2x-y+z=7

Answer 1

First, write this as an augmented matrix. Then use elementary row operations to transform it into reduced row echelon form. You start with:

[3, -6, 9 | 0] divide by 3
[4, -6, 8 | -4] add -4/3 row 1
[-2, -1, 1 | 7] add 2/3 row 1

[1, -2, 3 | 0] add row 2
[0, 2, -4 | -4] divide by 2
[0, -5, 7 | 7] add 5/2 row 2

[1, 0, -1 | -4] subtract 1/3 row 3
[0, 1, -2 | -2] subtract 2/3 row 3
[0, 0, -3 | -3] divide by -3

[1, 0, 0 | -3]
[0, 1, 0 | 0]
[0, 0, 1 | 1]

So the unique solution is x=-3, y=0, and z=1.

Answer 2

What is Gauss and Jordan. I know who Gauss is but are referring to a specific method??? If so please include. Off the top of my head I know I can solved this using either substitution or a matrix but if you are suppose to be using another method, fill us in.