Let W be the set of all vectors of the form [5s 3t 5s - 3t 4s + 5t] Show that W

Question

Let W be the set of all vectors of the form [5s 3t 5s - 3t 4s + 5t] Show that W is a subspace of R^4 by finding vectors u and v such that W = Span(u, v). write the vectors in W as column vectors. [5s 3t 5s - 3t 4s + 5t] = s [] + 1 [] = su + tv What does this imply about W? A. W = Span (s, t) B. W = Span (u, v) C. W = u + t D. W = u v Explain how this result shown that W is a subspace of R^4. Choose the correct answer below A. Since u and v are in R^4 and W = Span (u v), W is a subspace of R^4 B. Since u and v are in R^4 and W = u + v, W is a subspace of R^4 C. Since s and t are in R and W = u + v, W is a subspace of R^4 D. Since s and t are in R and W = Span (u v), W is a subspace of R^4

Explanation / Answer

Given W = .

To show: W is subspace of R4 , find vectors u and v such that W = Span(u,v)

Solution:

W = = s + t

So we can take u = and v =

Since W = span(u,v) which is a subset of R4

Therefore,

For the first multiple choice question the answer is option (B)

For the second multiple choice question the answer is option (A)

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