Let W be the set of all vectors of the form:

Question

Let W be the set of all vectors of the form:[2s+t 5s-4t 3s+2t 4s-t] Find vectors u and v such that W=Spanuv 

Answer 1

Since all vectors in W can be written as [2s+t 5s-4t 3s+2t 4s-t], we can rewrite the form as

s[2 5 3 4]+t[1 -4 2 -1].

Therefore, one simple choice for u,v is u = [2 5 3 4], v = [1 -4 2 -1].