SOLUTION: Solve the system of equations to the right using matrices. Use Gaussian elimination with back substitution or Gauss Jordan elimination. x + y + z= 9 x - y - z= -7 x -y + z = 1

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve the system of equations to the right using matrices. Use Gaussian elimination with back substitution or Gauss Jordan elimination. x + y + z= 9 x - y - z= -7 x -y + z = 1      Log On


   

Question 306818: Solve the system of equations to the right using matrices. Use Gaussian elimination with back substitution or Gauss Jordan elimination.
x + y + z= 9
x - y - z= -7
x -y + z = 1
The solution set is [_, _, _]
Found 2 solutions by JBarnum, richwmiller:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By%2Bz=9
x-y-z=-7
x-y%2Bz=1
by now you should know the elimination method, because that is what u need to know to solve this problem, the first 2 equations are perfect, so lets add them together
x%2By%2Bz=9
x-y-z=-7solve for x
2x%2B0%2B0=2divide by 2
x=1
take the second 2 equations and solve for y
x-y-z=-7
x-y%2Bz=1
_ _ _ _ _ _ _
1-y-z=-7
1-y%2Bz=1add the equations together
2-2y%2B0=6
-2y=4
y=-2
_ _ _ _ _ _ _
x%2By%2Bz=9
1-2%2Bz=9
-1%2Bz=9
z=10
The solution set is [1,-2,10]

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!

add down (-1/1) *row 1 to row 2
1,1,1,9
0,-2,-2,-16
1,-1,1,1


add down (-1/1) *row 1 to row 3
1,1,1,9
0,-2,-2,-16
0,-2,0,-8


divide row 2 by -2/1
1,1,1,9
0,1,1,8
0,-2,0,-8


add down (2/1) *row 2 to row 3
1,1,1,9
0,1,1,8
0,0,2,8


divide row 3 by 2/1
1,1,1,9
0,1,1,8
0,0,1,4


add up (-1/1) *row 3 to row 2
1,1,1,9
0,1,0,4
0,0,1,4


add up (-1/1) *row 3 to row 1
1,1,0,5
0,1,0,4
0,0,1,4


add up (-1/1) *row 2 to row 1
1,0,0,1
0,1,0,4
0,0,1,4

final
1,0,0,1
0,1,0,4
0,0,1,4
x=1 y=4 z=4
(1,4,4)