SOLUTION: Hi again, can anyone show me how to use Gaussian Elimination? I have to use it to solve some of the following eqaution. Help with the whole equation would be most apreciated. Solv

Algebra ->  Systems-of-equations -> SOLUTION: Hi again, can anyone show me how to use Gaussian Elimination? I have to use it to solve some of the following eqaution. Help with the whole equation would be most apreciated. Solv      Log On


   

Question 214357: Hi again, can anyone show me how to use Gaussian Elimination? I have to use it to solve some of the following eqaution. Help with the whole equation would be most apreciated.
Solve the following system of equations by hand. Use the Gaussian Elimination, on the augmeted matrix, and write the row operation you used next to each row.
system%282x+%2B+y+-+z+=+3%2Cx+-+y+%2B+z+=+0%0D%0A%2Cy+%2B+2z+=+1%29
Help with steps and added notes would be really appreciated.
-Nick.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
system%282x+%2B+y+-+z+=+3%2Cx+-+y+%2B+z+=+0%0D%0A%2Cy+%2B+2z+=+1%29 



Swap row 1 and 2 to get a 1 in the upper left corner



Multiply Row 1 temporarily by -2, getting 

%28matrix%281%2C+5%2C+-2%2C2%2C+-2%2C+%22%7C%22%2C+0%29%29
and add that to row 2:
  
Swap rows 2 and 3:

 

Multiply Row 2 temporarily by -3, getting 

%28matrix%281%2C+5%2C+0%2C+-3%2C+-6%2C+%22%7C%22%2C+-3%29%29
and adding that to row 3:

 

Mutiply row 3 by -1%2F9

 

Convert back into a system of equations:

system%28x-y%2Bz=0%2C+0x%2B1y%2B2z=1%2C0x%2B0y%2B1z=0%29

or just

system%28x-y%2Bz=0%2C+y%2B2z=1%2Cz=0%29

Substitute z=0 from the bottom equation
into the middle equation y%2B2z=1

y%2B2%280%29=1
y%2B0=1
y=1

Substitute z=0 and y=1
into the top equation x-y%2Bz=0

x-%281%29%2B%280%29=0
x-1=0
x=1

So the solution is %22%28x%2Cy%2Cz%29%22=%22%281%2C1%2C0%29%22

Edwin