SOLUTION: Solve the system by Gaussian elimination. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter a general solution in terms of one of the

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system by Gaussian elimination. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter a general solution in terms of one of the      Log On


   

Question 1129786: Solve the system by Gaussian elimination. (If there is no solution, enter NO SOLUTION. If there are an infinite number of solutions, enter a general solution in terms of one of the variables.)
x + y + z = 0
2x − y + 3z= 0
x − z= 6
Thank you so much for your help!

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Your matrix:



Find the pivot in the 1st column in the 1st row:




Eliminate the 1st column:


Find the pivot in the 2nd column (inversing the sign in the whole row) and swap the 3rd and the 2nd rows



Eliminate the 2nd column




Make the pivot in the 3rd column by dividing the 3rd row by 7





Eliminate the 3rd column

Solution set:
x%5B1%5D+=+24%2F7
x%5B2%5D+=+-6%2F7
x%5B3%5D+=+-18%2F7