SOLUTION: how do you make a system of three linear equations in three variables for which the solution set is (0,0,0)? why is the set called homogeneous system?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: how do you make a system of three linear equations in three variables for which the solution set is (0,0,0)? why is the set called homogeneous system?      Log On


   



Question 910867: how do you make a system of three linear equations in three variables for which the solution set is (0,0,0)? why is the set called homogeneous system?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By%2Bz=0
x%2By-z=0
x-y%2Bz=0
Any system that has the zero vector as the right hand side is a homogeneous system which means the zero vector is always a solution.
If the matrix is not singular, it's the only solution, like in this case.