SOLUTION: x+2y-2z=2
3x-2y+2z=-1
x-2y-z=0
A
The unique solution to the system is left
The system has infinitely many solutions. The solution described in terms of variable z is
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Question 1086862: x+2y-2z=2
3x-2y+2z=-1
x-2y-z=0
A
The unique solution to the system is left
The system has infinitely many solutions. The solution described in terms of variable z is
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
x+2y-2z=2
3x-2y+2z=-1
x-2y-z=0
A
The unique solution to the system is left
The system has infinitely many solutions. The solution described in terms of variable z is
Solution:
x+2y-2z=2............(1)
3x-2y+2z=-1..........(2)
x-2y-z=0.............(3)
(1)+(2) =>
4x=1 => x=1/4
(1)+(3)
2x-3z=2 =>
2/4-3z=2 [x=1/4] =>
3z=-1/2
Substitute x and z in (1)
1/4+2y-2(-1/2)=2 =>
2y=2-1/4-1=3/4 =>
y=3/8
Therefore there is a unique solution set, S={1/4, 3/8, -1/2}
This conclusion can also be obtained by seeing that the three equations are not linearly dependent.
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