Question 151663
Let's say that we have the system


{{{system(3x+2y+5z=10,x+3y+6z=13,12x+2y+4z=14)}}}



You can write this system in a more compact form by ignoring the variables and focusing on the coefficients like this:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/augmentedmatrix2.png" alt="Photobucket - Video and Image Hosting">


Note: I simply wrote each coefficient in each element of the matrix. So for the first row I took the coefficients 3,2, and 5 and the value on the right side 10 and wrote them in the first row.



The reason why it's called an "augmented" matrix, is because the original matrix (the left hand matrix) is joined with the right hand column  to form a new "augmented" matrix.