SOLUTION: Solve the following system of equations using Gauss-Jordan elimination. Show all your steps. x + 2y + 3z = 1 y + 4z = 2 −x + y + z = 3

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following system of equations using Gauss-Jordan elimination. Show all your steps. x + 2y + 3z = 1 y + 4z = 2 −x + y + z = 3      Log On


   

Question 1017017: Solve the following system of equations using
Gauss-Jordan elimination. Show all your steps.
x + 2y + 3z = 1
y + 4z = 2
−x + y + z = 3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
x + 2y + 3z = 1
y + 4z = 2
-x + y + z = 3




R1+R3->R3



-3R2+R3->R3

             0 -3 -12 | -6
             0  3   4 |  4
             -------------
             0  0  -8 | -2



(-1/8)R3->R3




-2R2+R1->R1

             0 -2 -8 | -4
             1  2  3 |  1
             -------------
             1  0 -5 | -3

   

5R3+R1->R1

             0  0   5 | 5/4
             1  0  -5 | -3
             --------------
             1  0   0 |-7/4

   
             
-4R3+R2->R2

             0  0  -4 | -1
             0  1   4 |  2
             --------------
             0  1   0 |  1





system%28x=-7%2F4%2Cy=1%2Cz=expr%281%2F4%29%29

%28matrix%281%2C5%2Cx%2C%22%2C%22%2Cy%2C%22%2C%22%2Cz%29%29%22%22=%22%22%28matrix%281%2C5%2C-7%2F4%2C%22%2C%22%2C1%2C%22%2C%22%2C1%2F4%29%29

Edwin