SOLUTION: Use Gauss-Jordan elimination to solve the following system of equations. x+y+z=2 2x-3y+z=-11 -x+2y-z=8

Algebra ->  Matrices-and-determiminant -> SOLUTION: Use Gauss-Jordan elimination to solve the following system of equations. x+y+z=2 2x-3y+z=-11 -x+2y-z=8      Log On


   

Question 958270: Use Gauss-Jordan elimination to solve the following system of equations.
x+y+z=2
2x-3y+z=-11
-x+2y-z=8
Found 2 solutions by MathLover1, LinnW:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Your matrix
%28matrix%283%2C4%2C1%2C1%2C1%2C2%2C+2%2C-3%2C1%2C-11%2C-1%2C2%2C-1%2C8%29%29

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


%28matrix%283%2C4%2C1%2C1%2C1%2C2%2C+2%2C-3%2C1%2C-11%2C-1%2C2%2C-1%2C8%29%29


Eliminate the 1st column
%28matrix%283%2C4%2C1%2C1%2C1%2C2%2C+0%2C-5%2C-1%2C-15%2C0%2C3%2C0%2C10%29%29

Make the pivot in the 2nd column by dividing the 2nd row by -5


%28matrix%283%2C4%2C1%2C1%2C1%2C2%2C+0%2C1%2C1%2F5%2C3%2C0%2C3%2C0%2C10%29%29

Eliminate the 2nd column

%28matrix%283%2C4%2C1%2C0%2C4%2F5%2C-1%2C+0%2C1%2C1%2F5%2C0%2C0%2C3%2C-3%2F5%2C1%29%29


Make the pivot in the 3rd column by dividing the 3rd row by -3%2F5

%28matrix%283%2C4%2C1%2C0%2C4%2F5%2C-1%2C+0%2C1%2C1%2F5%2C3%2C0%2C0%2C1%2C-3%2F5%29%29


Eliminate the 3rd column
%28matrix%283%2C4%2C1%2C0%2C0%2C1%2F3%2C+0%2C1%2C0%2C10%2F3%2C0%2C0%2C1%2C-3%2F5%29%29
x+=+1%2F3
y+=+10%2F3
z=+-5%2F3

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
The beginning matrix is
1 1 1 2
2 -3 1 -11
-1 2 -1 8
add 1 times the 1st row to the 3rd row
1 1 1 2
2 -3 1 -11
0 3 0 10
add -2 times the 1st row to the 2nd row
1 1 1 2
2 -5 -1 -15
0 3 0 10
add 3/5 times the 2nd row to the 3rd row
1 1 1 2
0 -5 -1 -15
0 0 -3/5 1
multiply the 3rd row by -5/3
1 1 1 2
0 -5 -1 -15
0 0 1 -5/3
add -1 times the 3rd row to the 1st row
1 1 0 11/3
0 -5 -1 -15
0 0 1 -5/3
add -1 times the 3rd row to the 2nd row
1 1 0 11/3
0 -5 0 -50/3
0 0 1 -5/3
multiply the 2nd row by -1/5
1 1 0 11/3
0 -5 0 -50/3
0 0 1 -5/3
add 1 times the 3rd row to the 2nd row
1 1 0 11/3
0 1 0 10/3
0 0 1 -5/3
add -1 times the 2nd row to the 1st row
1 0 0 1/3
0 1 0 10/3
0 0 1 -5/3