Vector Spaces and Scalar Multiplication Quiz
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Questions and Answers

What is the extra structure of multiplication by a scalar called on an abelian group?

  • Scaling (correct)
  • Real numbers
  • Addition
  • Binary operation

    • What is the binary operation defined on R3?

  • Subtraction
  • Multiplication
  • Addition (correct)
  • Division

    • How is the operation (α, v) denoted?

  • v*α
  • α.v (correct)
  • α*v
  • v/α

    • What is the result of α.(β.v) according to the given example?

    <p>(αβ).v</p> Signup and view all the answers

    What is the abelian group (R3, ∗) together with the rule of scaling called?

    <p>Vector space</p> Signup and view all the answers

    What is the defining property of the scaling operation on R3?

    <p>The scaling operation satisfies the properties: 1. α.v = v, 2. α.(β.v) = (αβ).v, 3. α.(v ∗ w) = α.v ∗ α.w, 4. (α + β).v = α.v ∗ β.v</p> Signup and view all the answers

    How is the operation (α, v) denoted?

    <p>The operation (α, v) is denoted by α.v</p> Signup and view all the answers

    What are the properties of the scaling operation on R3?

    <p>The properties of the scaling operation on R3 are: 1. α.v = v, 2. α.(β.v) = (αβ).v, 3. α.(v ∗ w) = α.v ∗ α.w, 4. (α + β).v = α.v ∗ β.v</p> Signup and view all the answers

    What is the name of the abelian group (R3, ∗) together with the rule of scaling?

    <p>The abelian group (R3, ∗) together with the rule of scaling is called a vector space.</p> Signup and view all the answers

    What are the defining properties of the scaling operation on R3?

    <p>The defining properties of the scaling operation on R3 are: 1. α.v = v, 2. α.(β.v) = (αβ).v, 3. α.(v ∗ w) = α.v ∗ α.w, 4. (α + β).v = α.v ∗ β.v</p> Signup and view all the answers

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