Problem:

Find three vectors in R3 which are linearly dependent, and are such that any two of them are linearly independent.

What I have so far:

{v1, v2, v3} is a linearly dependent set.

{v1, v2} is a linearly independent set.

{v2, v3} is a linearly independent set.

{v1, v3} is a linearly independent set.

a*v1 + b*v2 + c*v3 = 0, where not all a, b, and c = 0 due to linearly dependence.

If a is not 0 then, v1 = - [ ( b*v2 + c*v3 ) / a ]

If b is not 0 then, v2 = - [ ( a*v1 + c*v3 ) / b ]

If c is not 0 then, v3 = - [ ( a*v1 + b*v2 ) / c ]

And, I am stuck. I don't know what to do after this, much less use this to find three vectors in R3 that satisfy this.

Thank you in advance,

-Z