The system of linear equations has a unique solution. Find the solution using Ga

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The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.
 
2y + z = 8
x + y = 8
3x + 3y − z = 12
(xyz) = 
 
 
Jul 17th, 2015

Thank you for the opportunity to help you with your question!

2y + z = 8

x + y = 8

3x + 3y - z = 12

First, we write the matrix and we use row operations.

0    2    1    8

1    1    0    8

3    3   -1   12

Exchange Row 2 and Row 1.    R2 <---> R1

1    1    0    8

0    2    1    8

3    3   -1   12

New R3 = R3 - 3*R1

1    1   0   8

0    2   1   8

0    0   -1  -12

New R2 = 1/2R2

1    1    0    8

0    1   1/2   4

0    0    -1   -12

New R1 = R1 - R2

1    0    -1/2    4

0    1     1/2    4

0    0      -1   -12

New R3 = -1*R3

1   0   -1/2   4

0    1   1/2   4

0    0     1    12

New R1 = R1 + 1/2*R3    ;   New R2 = R2 - 1/2*R3

1   0    0    10

0    1    0    -2

0    0    1    12

So finally, we would have:

(x , y, z) = (10, -2, 12)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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