If you calculate the determinant of [v1 v2 v3] it equals zero, which means the values are not linearly independent. It actually reduces to the equations:

-2x+y-6z = -1

Y+4z= 3

Y+4z=3

Since the last two equations are the same this means there a infinite number of solutions. For example both (-2,3,0) and (-3,-1, 1) are solutions.

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