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?

  • 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?

    <p>mn</p> Signup and view all the answers

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

    <p>The zero transformation</p> Signup and view all the answers

    Which one of these is the most correct?

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

    Which one of these is the most correct?

    <p>(f + g)(v) = f(v) + g(v)</p> Signup and view all the answers

    Which one of these is the most correct?

    <p>(k · f)(v) = k · f(v)</p> Signup and view all the answers

    Which one of these is the most correct?

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

    Which one of these is the most correct?

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

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