Gauss - Jordan Elimination

Gaussian elimination gives us tools to solve large linear systems numerically. It is done by manipulating the given matrix using the elementary row operations to put the matrix into row echelon form. To be in row echelon form, a matrix must conform to the following criteria:

1. If a row does not consist entirely of zeros, then the first non zero number in the row is a 1.(the leading 1)
2. If there are any rows entirely made up of zeros, then they are grouped at the bottom of the matrix.
3. In any two successive rows that do not consist entirely of zeros, the leading 1 in the lower row occurs farther to the right that the leading 1 in the higher row.

It is now obvious, by inspection, that the solution to this linear system is x=3, y=1, and z=2. Again, by solution, it is meant the x, y, and z required to satisfy all the equations simultaneously.

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* I've no idea the reason why I am posting this such kind of thing (taking from the subject Linear Algebra). But the most important thing right now is, how I'm gonna encountering my problem in mastering this subtopic? This subtopic is so burdening me and I'm wonder, after all the failure trial that I've done in doing the exercises...when I will master this topic successfully? God, please help me.. I don't want to lose 5 and more marks just because of this killing point. Please give me the chance for me to improve myself before the dead line comes.. Amin.. (-_-")