# Let W be the set of all vectors of the form: -2s-2t -5s+4t -s-2t . Find vectors u and vector v such that W = Span{vector u, vector v}

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Expert Answers

sciencesolve | Certified Educator

You need to use the definition of span of collection of vectors such that:

`bar v in bar W if bar v = alpha*<-2s - 2t, -5s + 4t, -s - 2t>`

`bar u in bar W if bar u = beta*<-2s - 2t, -5s + 4t, -s - 2t>`

If `bar v = <a,b,c>` and `bar u = <d,e,f>` in span `bar W` yields:

`{(a = alpha*(-2s - 2t)),(b = alpha*(-5s + 4t)),(c = alpha*(-s - 2t)):}`

`{(d = beta*(-2s - 2t)),(e = beta*(-5s + 4t)),(f = beta*(-s - 2t)):}`

**Hence, evaluating the vectors `bar u` and `bar v` , in span `bar W` , yields **`bar u = < alpha*(-2s - 2t),alpha*(-5s + 4t),alpha*(-s - 2t)>, bar v = <beta*(-2s - 2t),beta*(-5s + 4t),beta*(-s - 2t)>.`