##### 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.

 x − 2y + z = 1 y + 2z = 9 x + y + 3z = 20
(xyz) =
−1.5, 2, 6.5

Jul 17th, 2015

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x - 2y + z = 1

y + 2z = 9

x + y + 3z = 20

Gauss-Jordan elimination

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

1    -2    1     1

0     1     2     9

1      1    3    20

New R3 = R3 - R1

1    -2    1     1

0     1    2     9

0     3    2     19

New R1 = R1 + 2*R2     ;   New R3 = R3 - 3R2

1    0     5     19

0    1     2      9

0    0    -4     -8

New R3 = -1/4*R3

1    0    5    19

0    1    2     9

0    0    1     2

New R1 = R1 - 5*R3   ;    New R2 = R2 - 2*R3

1    0     0    9

0    1     0     5

0    0     1    2

The last column would be the values of x, y, and z. So our final answer would be:

(x, y, z) = (9 , 5 , 2)

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

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Jul 17th, 2015
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Jul 17th, 2015
Sep 19th, 2017
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