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Let H be the set of all vectors of the form egin{bmatrix} -2t \ t \ 3t end{bmatrix}. Find a vector v in R^3 such that H = Span{v}. Why does this show that H is a subspace of R^3? H = Span{v} for v = Box Why does this show that H is a subspace of R^3? A. Since the zero vector of R^3 is not in Span{v}, H is a subspace of R^3. B. Since v is in R^3, H = Span{v} is a subspace of R^3. C. Since R^3 = Span{v}, H = Span{v} is a subspace of R^3. D. Since v spans R^3 and v spans H, H spans R^3.

          Let H be the set of all vectors of the form egin{bmatrix} -2t \ t \ 3t end{bmatrix}. Find a vector v in R^3 such that H = Span{v}. Why does this show that H is a subspace of R^3?

H = Span{v} for v = Box

Why does this show that H is a subspace of R^3?

A. Since the zero vector of R^3 is not in Span{v}, H is a subspace of R^3.
B. Since v is in R^3, H = Span{v} is a subspace of R^3.
C. Since R^3 = Span{v}, H = Span{v} is a subspace of R^3.
D. Since v spans R^3 and v spans H, H spans R^3.

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Let H be the set of all vectors of the form eginbmatrix -2t t 3t endbmatrix. Find a vector v in R^3 such that H = Spanv. Why does this show that H is a subspace of R^3?

H = Spanv for v = Box

Why does this show that H is a subspace of R^3?

A. Since the zero vector of R^3 is not in Spanv, H is a subspace of R^3.
B. Since v is in R^3, H = Spanv is a subspace of R^3.
C. Since R^3 = Spanv, H = Spanv is a subspace of R^3.
D. Since v spans R^3 and v spans H, H spans R^3.

Added by Patrick D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

06/16/2022

Step 1

This means that every vector in H can be written as a scalar multiple of v. Since the question does not provide specific vectors in H, we can't find a specific v. However, we can say that v is any non-zero vector in H. Now, why does this show that H is a subspace Show more…

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Let H be the set of all vectors of the form [-2t, t, 3t]. Find a vector v in R^3 such that H = Span{v}. Why does this show that H is a subspace of R^3? H = Span{v} for v = Why does this show that H is a subspace of R^3? A. Since the zero vector of R^3 is not in Span{v}, H is a subspace of R^3. B. Since v is in R^3, H = Span{v} is a subspace of R^3. C. Since R^3 = Span{v}, H = Span{v} is a subspace of R^3. D. Since v spans R^3 and v spans H, H spans R^3.

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