SOLUTION: solve the homogeneous system: {2x+y+z=0 4x-5y+z=0 3x-2y+z=0

Algebra.Com
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..

RELATED QUESTIONS

solve the following homogeneous system of linear equations: x+y-3y+2w=0, 2x-y+2z-3w=0, (answered by Alan3354)
solve the following homogeneous systeam of linear equations: x+y-3y+2w=0,... (answered by Alan3354)
solve homogeneous system of equations x - 2y + 3z = 0 3x - 7y - 4z = 0 4x - 4y + z = (answered by Edwin McCravy)
Solve the system. 2X+Y-3Z=0 4x+2y-6Z=0... (answered by Alan3354)
Solve the following system. 2x + 4y + 3z = 2 x + 2y - z = 0 4x + y - z = 6 (answered by ikleyn)
solve the system x+y+z=-1 x-y+3z=-17 2x+y+z=-2 Solve the system x-y+2z=7... (answered by solver91311)
Solve the system of equations. 2x + y = 0 x - 3y + z = 0 3x + y - z = 0 (answered by AnlytcPhil)
Solve the following system of linear eqnations. x + y – 3z + 2w = 0 2x - y + 2z (answered by Fombitz)
Solve the system. 2x+2y+3z=10 3x+y-z=0 x+y+2z=6 x= y=... (answered by uday1435)