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Are the following statements true or false? 1. If {u, v, w} is a linearly independent set, then {2u + 2v + 5w, u + 2v, u +5w} is linearly independent.

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