SOLUTION: In the problem if there exist solutions of the homogeneous system of linear equations other than x=0, express the general solution as a linear combination of linearly independent c

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: In the problem if there exist solutions of the homogeneous system of linear equations other than x=0, express the general solution as a linear combination of linearly independent c      Log On


   

Question 293780: In the problem if there exist solutions of the homogeneous system of linear equations other than x=0, express the general solution as a linear combination of linearly independent column vectors.
x_1 + 2x_2 - x_3 = 0
2x_1 + x_2 + x_3 = 0
x_1 - x_2 + 2x_3 = 0

(x_1 means x subscript of 1)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
change
x_1 to x
x_2 to y
x_3 to z
x+2y-z=0,
2x+y+z=0,
x-y+2z=0
x=z-2y
z-2y=-y+2z
z=-y
y=-x
z=-x