What are linearly dependent vectors in 4-space?

[Dagger1]

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?

 

[Dick]

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.