SOLUTION: Solve the system of linear equations using the Gauss-Jordan elimination method. 3x + 2y − 2z = 15 2x − 2y + 3z = −3 4x − y + 3z = 3

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Question 702981: Solve the system of linear equations using the Gauss-Jordan elimination method.
3x + 2y − 2z = 15
2x − 2y + 3z = −3
4x − y + 3z = 3
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

  3      2     -2     15
  2     -2      3     -3
  4     -1      3      3

Swap: Row 1 and 2, and then 2 and 3.

  2     -2      3     -3
  4     -1      3      3
  3      2     -2     15

R1/2 to R1

  1     -1    3/2   -3/2
  4     -1      3      3
  3      2     -2     15

-4R1 + R2 to R2

  1     -1    3/2   -3/2
  0      3     -3      9
  3      2     -2     15

R2/4 to R2

  1     -1    3/2   -3/2
  0      1     -1      3
  3      2     -2     15

-3R1 + R3 to R3

  1     -1    3/2   -3/2
  0      1     -1      3
  0      5  -13/2   39/2
 
-5R2 + R3 to R3

  1     -1    3/2   -3/2
  0      1     -1      3
  0      0     -5     15

R3/-5 to R3

  1     -1    3/2   -3/2
  0      1     -1      3
  0      0      1     -3

R3 + R2 to R2

  1     -1    3/2   -3/2
  0      1      0      0
  0      0      1     -3

R2 + R1 to R1

  1      0    3/2   -3/2
  0      1      0      0
  0      0      1     -3

-3/2*R3 + R1 to R1

  1      0      0      3
  0      1      0      0
  0      0      1     -3

x = 3, y = 0, z = -3

John

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