Question 815171
You should not include so many problems (especially such labor-intensive ones) in a single post. I will do the first one for you. Re-post the others separately if you want more help.<br>
Note: Algebra.com's formula drawing software does not do matrices very well. So I am going to just show the rectangular array of numbers without the brackets which usually indicate a matrix.<br>
2x+4y+z=3
3x+2y-2z=-2
x-y+z=6
The augmented matrix:
<pre>
    2    4    1    3
    3    2   -2   -2
    1   -1    1    6
Replace row 1 with 1/2 times row 1:
    1    2    1/2    3/2
    3    2    -2    -2
    1   -1     1     6
Add -3 times row 1 to row 2:
    1    2    1/2      3/2
    0   -4   -7/2    -13/2
    1   -1     1       6
Add -1 times row 1 to row 3:
    1    2    1/2      3/2
    0   -4   -7/2    -13/2
    0   -3    1/2      9/2
Replace row 2 with -1/4 times row 2:
    1    2    1/2     3/2
    0    1    7/8    13/8
    0   -3    1/2     9/2
Add -2 times row 2 to row 1:
    1    0   -5/4    -7/4
    0    1    7/8    13/8
    0   -3    1/2     9/2
Add 3 times row 2 to row 3:
    1    0   -5/4    -7/4
    0    1    7/8    13/8
    0    0   25/8    75/8
Replace row 3 with 8/25 times row 3:
    1    0   -5/4    -7/4
    0    1    7/8    13/8
    0    0    1       3
Add 5/4 times row 3 to row 1
    1    0    0       2
    0    1    7/8     13/8
    0    0    1       3
Add -7/8 times row 3 to row 2:
    1    0    0       2
    0    1    0      -1
    0    0    1       3
</pre>This translates into:
x = 2
y = -1
z = 3