Exploring Dual Spaces and Linear Transformations

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Which set denotes the vector space of all linear transformations from V to W?

V ∗

L(V, W) (correct)

W ∗

L(V)

What is the formula for (f + g)(v)?

(f + g)(v) = f(v) - g(v)

(f + g)(v) = f(v) + g(v) (correct)

(f + g)(v) = f(v) / g(v)

(f + g)(v) = f(v) * g(v)

What is the formula for (k · f)(v)?

(k · f)(v) = k - f(v)

(k · f)(v) = k + f(v)

(k · f)(v) = k * f(v)

(k · f)(v) = k · f(v) (correct)

What is the dimension of the vector space L(V, W) if dim V = n and dim W = m?

mn Signup and view all the answers

What is the zero vector in L(V, W)?

The zero transformation Signup and view all the answers

Which one of these is the most correct?

The set of all linear transformations from V to W is denoted by L(V, W) Signup and view all the answers

Which one of these is the most correct?

(f + g)(v) = f(v) + g(v) Signup and view all the answers

Which one of these is the most correct?

(k · f)(v) = k · f(v) Signup and view all the answers

Which one of these is the most correct?

The zero vector in L(V, W) is the zero transformation Signup and view all the answers

Which one of these is the most correct?

The dimension of the vector space L(V, W) is mn if dim V = n and dim W = m Signup and view all the answers

Exploring Dual Spaces and Linear Transformations

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Questions and Answers

Which set denotes the vector space of all linear transformations from V to W?

What is the formula for (f + g)(v)?

What is the formula for (k · f)(v)?

What is the dimension of the vector space L(V, W) if dim V = n and dim W = m?

What is the zero vector in L(V, W)?

Which one of these is the most correct?

Which one of these is the most correct?

Which one of these is the most correct?

Which one of these is the most correct?

Which one of these is the most correct?

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