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Let H be the set of all points in the fourth quadrant in the plane R². That is, H = {(x, y) | x ≥ 0, y ≤ 0}. Is H a subspace of the vector space R²? y X Select true or false for each statement. 1. This set contains the zero vector: 2. This set is closed under vector addition: 3. This set is closed under scalar multiplication: 4. This set is a subspace:

Let H be the set of all points in the fourth quadrant in the plane R². That is, H = {(x, y) | x ≥ 0, y ≤ 0}. Is H a subspace of the vector space R²? y X Select true or false for each statement. 1. This set contains the zero vector: 2. This set is closed under vector addition: 3. This set is closed under scalar multiplication: 4. This set is a subspace:

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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Let H be the set of all points in the fourth quadrant in the plane R². That is, H = {(x, y) | x ≥ 0, y ≤ 0}. Is H a subspace of the vector space R²? Y X Select true or false for each statement. 1. This set contains the zero vector: 2. This set is closed under vector addition: 3. This set is closed under scalar multiplication: 4. This set is a subspace:
Transcribed Image Text:Let H be the set of all points in the fourth quadrant in the plane R². That is, H = {(x, y) | x ≥ 0, y ≤ 0}. Is H a subspace of the vector space R²? Y X Select true or false for each statement. 1. This set contains the zero vector: 2. This set is closed under vector addition: 3. This set is closed under scalar multiplication: 4. This set is a subspace:
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