What are linearly dependent vectors in 4-space?

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SUMMARY

The discussion centers on finding three linearly dependent vectors in R^4, specifically ensuring that the third vector, v3, is not in the span of the first two vectors, v1 and v2. The proposed vectors are v1 = [1,0,0,0], v2 = [0,1,0,0], and v3 = [0,0,1,0]. However, the conclusion drawn is that these vectors are linearly independent, as the only solution to the equation c1*v1 + c2*v2 + c3*v3 = 0 is c1 = c2 = c3 = 0, contradicting the requirement for linear dependence.

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Homework Statement

Find three vectors in R^4 (none of which are the zero vector) such that they are linearly dependent and v3 is not in the Span of v1&v2.The attempt at a solution

My answer was v1=[1,0,0,0] v2=[0,1,0,0] & v3=[0,0,1,0]

Does this work? v3 is not in the span of v1&v2. If placed in a matrix set equal to zero, there is a free variable x4. So aren't they linearly dependent?
 
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No, they are linearly independent. c1*v1+c2*v2+c3*v3=0 has c1=c2=c3=0 as it's only solution. Nothing in the problem said v1 and v2 have to be linearly independent.
 

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