SOLUTION: Write the augmented matrix of the system to use the matrix method to solve the system. x+2y-3z=15 2x-3y+z=-12 -x+y-3z=15

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Question 818221: Write the augmented matrix of the system to use the matrix method to solve the system.
x+2y-3z=15
2x-3y+z=-12
-x+y-3z=15
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
There are several matrix-based methods for solving systems of equations like this. So I'm not sure what is meant by "the matrix method". I hope the following seems familiar. (Note: algebra.com does not do the brackets around matrices well. So I am going to show just the array of numbers.)
Initial matrix.
     1     2    -3    15
     2    -3     1   -12
    -1     1    -3    15
Add -2 times row 1 to row 2
     1     2    -3    15
     0    -7     7   -42
    -1     1    -3    15
Add 1 times row 1 to row 3
     1     2    -3    15
     0    -7     7   -42
     0     3    -6    30
Replaced row 2 with -1/7 times row 2.
    1    2   -3   15
    0    1   -1    6
    0    3   -6   30
Add -2 times row 2 to row 1
    1    0   -1    3
    0    1   -1    6
    0    3   -6   30
Add -3 times row 2 to row 3.
    1    0   -1    3
    0    1   -1    6
    0    0   -3   12
Replaced row 3 with -1/3 times row 3.
    1    0   -1    3
    0    1   -1    6
    0    0    1   -4
Add 1 times row 3 to row 1.
    1    0    0   -1
    0    1   -1    6
    0    0    1   -4
Add 1 times row 3 to row 2.
    1    0    0   -1
    0    1    0    2
    0    0    1   -4
which translates into:
x = -1
y = 2
z = -4