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I'm presented with a set of vectors in [itex]\mathbb{R}^{3}[/itex]

[itex]v_1 = (a_1,a_2,a_3)[/itex] [itex]v_2 = (b_1,b_2,b_3)[/itex] and [itex]v_3 = (c_1,c_2,c_3)[/itex]

I'm suppose to determain if these vectors are linear independent.

My question is: The most simple way of proving the above is that written the vectors as a set of linear combinations ?

[itex] a_1 x + a_2 y + a_3 z = 0 [/itex]

[itex] b_1 x + b_2 y + b_3 z = 0 [/itex]

[itex] c_1 x + c_2 y + c_3 z = 0 [/itex]

/Fred