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# Vector Spaces and Scalar Multiplication Quiz

Created by
@EncouragingAlexandrite

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

• Scaling (correct)
• Real numbers
• Binary operation
• ### What is the binary operation defined on R3?

• Subtraction
• Multiplication
• 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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