S.O.S. Mathematics CyberBoard

I'm lost on how to complete them using matrices. It would be nice to have a step by step explanation if it's possible. The guide that was available on the site had a different way than what my professor tried to show. And the guide on the site was VERY simple, it didn't help with the problems that I was assigned. (Notably the first row, it was just all 1's and didn't help all that much.)

Ex.
2x + 6y + 3z = -20
5x - 3y - 5z = 47
4x + 3y + 2z = 4

The site had me try to get the Matrix to look something like this...
| 1 0 0 : a |
| 0 1 0 : b |
| 0 0 1 : c |

As my professor wanted just wanted it to look something like this...
| 1 * * : * |
| 0 1 * : * |
| 0 0 1 : * |
Where * is any number. (Not sure if it has to be any real number or not)

I'm not sure what to work on, especially since I just end up getting my work wrong because I end up working on it too much. But for the most part I just need to understand the steps into it.

(Didn't see the matrix algebra section until just now... please move this there.)

That is just the difference between row echelon and reduced row echelon form.

Once you have row echelon form it is easy to get to reduced form (as you essential already know one of x,y,z)

This is just Gauss-Jordan elimination - a quick google should help out

Do you know how to solve these by elimination or substitution?

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I'm not prejudiced...I hate everybody equally!

Yes, I do. But the problems is REQUIRED to be solved using the Matrix method mainly.