Question 64350: solve the homogeneous system: {2x+y+z=0
4x-5y+z=0
3x-2y+z=0
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! solve the homogeneous system:
2x+y+z=0..........................1
4x-5y+z=0....................2
3x-2y+z=0................3
EQN.2-EQN.1
2X-6Y=0......OR.......X-3Y=0........................4
EQN.3-EQN.1
X-3Y=0......................5
EQN.4 & EQN.5 ARE IDENTICAL.HENCE THE SYSTEM IS CONSISTENT AND DEPENDENT.
SO SOLUTION SET IS
FROM EQN.4
X=3Y
PUTTING IN EQN.1
6Y+Y+Z=0
7Y+Z=0
Z=-7Y...
HENCE ANY SET OF THE TYPE
3Y,Y,-7Y....FOR ANY VALUE OF Y IS A SOLUTION SET..EX...(3,1,-7),(9,3,-21)...ETC..
|
|
|
