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Are the following statements true or false? 1. The basis for the zero vector space {0} consists of the zero vector itself. 2. The intersection of two subspaces of a vector space is always a subspace. 3. A proper subset of a linearly independent set can sometimes form a spanning set. 4. If {u, v, w} is a linearly independent set, then {u+ 4v, v - 5w, w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {2u + 4v + 5w, u + 4v, u + 5w} is linearly independent.

Are the following statements true or false? 1. The basis for the zero vector space {0} consists of the zero vector itself. 2. The intersection of two subspaces of a vector space is always a subspace. 3. A proper subset of a linearly independent set can sometimes form a spanning set. 4. If {u, v, w} is a linearly independent set, then {u+ 4v, v - 5w, w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {2u + 4v + 5w, u + 4v, u + 5w} is linearly independent.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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? ? ? ? ? Are the following statements true or false? 1. The basis for the zero vector space {0} consists of the zero vector itself. 2. The intersection of two subspaces of a vector space is always a subspace. 3. A proper subset of a linearly independent set can sometimes form a spanning set. 4. If {u, v, w} is a linearly independent set, then {u+ 4v, v − 5w, w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {2u + 4v + 5w, u + 4v, u + 5w} is linearly independent.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false? 1. The basis for the zero vector space {0} consists of the zero vector itself. 2. The intersection of two subspaces of a vector space is always a subspace. 3. A proper subset of a linearly independent set can sometimes form a spanning set. 4. If {u, v, w} is a linearly independent set, then {u+ 4v, v − 5w, w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {2u + 4v + 5w, u + 4v, u + 5w} is linearly independent.
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