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 + y + 6z = 7
x + y + 3z = 7
x + 2y + 4z = 7
(xyz) = 
 
 
Jul 17th, 2015

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

x + y + 6z = 7

x + y + 3z = 7

x + 2y + 4z = 7

First, we write the matrix and use row operations.

1    1    6    7

1    1    3    7

1    2    4    7

New R2 = R2 - R1   ;   New R3 = R3 - R1

1    1    6   7

0    0   -3   0

0    1    -2   0

Exchange Row 2 and Row3.    R2 <---> R3

1    1   6   7

0    1   -2   0

0    0   -3   0

New R1 = R1 - R2

1    0    8    7

0    1    -2   0

0    0    -3   0

New R3 = -1/3R3

1   0   8    7

0   1   -2   0

0   0    1   0

New R1 = R1 - 8*R3    ;   New R2 = R2 + 2*R3

1   0    0   7

0   1    0   0

0   0    1   0

So finally, we have:

(x , y, z) = (7, 0, 0)

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

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