Show if its a lin. independent subset

[holezch]

Homework Statement

$$V = { (x_{1},x_{2},x_{3},x_{4},x_{5}) \in R^{5} : x_{1} -2x_{2} + 3x_{3} - x_{4} + 2x_{5} = 0 }$$

show that S = { (0,1,1,1,0) } is a linearly independent subset of V.

The Attempt at a Solution

I don't get it.. it's a set with 1 non zero vector, it's going to be linearly independent? then do I just have to show that it's actualy in V?

thanks

 

[VeeEight]

Yes, a set with 1 element is going to be linearly independent. You must verify that (0,1,1,1,0) is actually in V to show that S is a subset of V. Just plug the vector into the equation and see if you get 0.

 

[holezch]

thanks, I thought I was misunderstanding something.. since it looked to trivial to me haha