1. Write the augmented matrix for the given system: 

 x +  y + 2z = 6
3x + 2y +  z = 9
 x -  y      = 4 

Put in 1 coefficients, and "+ 0z" in the last equation.

1x + 1y + 2z = 6
3x + 2y + 1z = 9
1x - 1y + 0z = 4

Erase all the letters, replace the ='s by |'s, and
put brackes around:

[1  + 1  + 2  | 6]
[3  + 2  + 1  | 9]
[1  - 1  + 0  | 4]

Place the signs closer to the numbers

[1  +1  +2  | 6]
[3  +2  +1  | 9]
[1  -1  +0  | 4]

Erase the + signs:

[1   1   2  | 6]
[3   2   1  | 9]
[1  -1   0  | 4]

That's the augmented matrix. 

2. Use the system in problem #1. Without 
interchanging any of the rows in the augmented 
matrix, what is the first value which will be 
replaced with zero when using the Gaussian 
Elimination method?

The first value to be replaced by 0 is the 3.

It will be replaced by 0 by taking the
1st row  [1   1   2  | 6], multiplying it
thru by -3, getting [-3 -3 -6  | -18], then
adding that to row 2 like this
         [ 3  2  1  |   9]
         [-3 -3 -6  | -18] 
         ------------------
         [ 0 -1 -5  |  -9]

and then replace the second row by that:

[1   1   2  |  6]
[0  -1  -5  | -9]
[1  -1   0  |  4]

Edwin