Question

Use the Gauss-Jordan method to find all the solutions of the system
-3x1 +2x2 -x3 +6x4 = -7
7x1 -3x2 +2x3 -11x4 = 14
x1 -x4 = 1

It is a 3x5 matrix
-3 2 -3 6 -7
7 -3 2 -11 14
1 0 0 -1 1

Using the Gauss-Jordan method,
I got
1 0 0 -1 1
0 1 0 2 5/3
0 0 1 1 2

Yet when I verify it using an online calculator it give me this
1 0 0 -1 1
0 1 0 2 -1
0 0 1 1 2

------
I retry doing it and I still cant get the -1 on the 2nd row last column

Answer 1

You have 4 variables but only 3 equations, so you can't expect a unique solution.
Since the steps to follow in GJ are not unique, I can't know how you arrived at it.
Here is a neat webpage that let's you see the steps
https://matrix.reshish.com/gauss-jordanElimination.php

notice the make x4 the independant variable, that is, let x4 be anything you want.
Check it out.

Answer 2

I found the error.. I keep doing those calculation error its irritating .__.

Thx Reiny

Answer 3

Solve the following system of linear equation by Gauss Jorden Method
3x1 + x2 + x3 + x4 = 0
5x1 − x2 + x3 − x4 = 0

Answer 4

3x+y=16
2x-27=4

Answer 5

3x+2y=16
2x-27=4