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The matrix should look like this: (this site has only 3x3 matrix).  


The first row consists of coefficients of first equation.
The second row consists of coefficients of second equation.
The third row consists of coefficients of equation 3.

To the right of the matrix, add the column for the following (to accompany each row:


The you may solve by back substitution. The solutions are:

x = 3
y = 1
z = 2

Substitute the values for x, y and z in each equation, and you'll find the these are the solutions.