I've attached the problem below.

The question asks me to find vectors u and v (in R^3) such that u+v is equal to a vector w with the form

|2b+4c |

| b |

| c |

In my approach, I first evaluated the span{u,v}.

If u=|u1 u2 u3|^T and v=|v1 v2 v3|^T. I don't understand why they are asking me for a specific vector u and v. Couldn't I just let either u2 and u3 or v2 and v3 be zero and u2 and u3 or v2 and v3 not picked be 1?