Determine if the following homogeneous system has a nontrivial solution. Then describe the solution set.
3x_{1} + 5x_{2} - 4x_{3} = 0
-3x_{1} - 2x_{2} + 4x_{3} = 0
6x_{1} + x_{2} - 8x_{3} = 0
Determine if the following homogeneous system has a nontrivial solution. Then describe the solution set.
3x_{1} + 5x_{2} - 4x_{3} = 0
-3x_{1} - 2x_{2} + 4x_{3} = 0
6x_{1} + x_{2} - 8x_{3} = 0