SOLUTION: Use the Gauss - Jordan method to solve the following system of equations. 2x + y - z = -1 x

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Question 316592: Use the Gauss - Jordan method to solve the following system of equations.
2x + y - z = -1
x - 2y + 2z = 7
3x + y + z = 4
Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
Use the Gauss - Jordan method to solve the following system of equations.
2x + y - z = -1
x - 2y + 2z = 7
3x + y + z = 4
-----
write out the coefficients and the constant as follows:
x y z c
2 1 -1 -1
1 -2 2 7
3 1 1 4 (add row 3 to row 1)
-----------------
5 2 0 3 (add row 1 to row 2)
1 -2 2 7
3 1 1 4
-----------------
5 2 0 3
6 0 2 10
3 1 1 4 (multiply row 3 by -2)
-----------------
5 2 0 3
6 0 2 10 (add row 2 to row 3)
-6 -2 -2 -8
----------------
5 2 0 3
6 0 2 10
0 -2 0 2 (add row 3 to row 1)
----------------
5 0 0 5 (divide row 1 by 5)
6 0 2 10 (divide row 2 by 2)
0 -2 0 2 (divide row 3 by -2)
----------------
1 0 0 1 (multiply row 1 by -3)
3 0 1 5
0 1 0 -1
----------------
-3 0 0 -3 (add row 1 to row 2)
3 0 1 5
0 1 0 -1
----------------
-3 0 0 -3 (lastly divide row 1 by -3)
0 0 1 2
0 1 0 -1
----------------
1 0 0 1
0 0 1 2
0 1 0 -1 (rearrange these 3 rows)
-----------------
1 0 0 1
0 1 0 -1
0 0 1 2
-----------------
we wanted to get to the last matrix shown, it is the identity matrix, it has a nice neat diagonal of 1's and the answers are all in the last column
x = 1
y = -1
z = 2
check:
2x + y - z = -1
x - 2y + 2z = 7
3x + y + z = 4
2(1) + (-1) - (2) = 2 - 1 - 2 = 2 - 3 = -1
(1) - 2(-1) + 2(2) = 1 + 2 + 4 = 7
3(1) + (-1) + (2) = 3 - 1 + 2 = 2 + 2 = 4

SOLUTION: Use the Gauss - Jordan method to solve the following system of equations. 2x + y - z = -1 x - 2y + 2z = 7 3x + y + z = 4