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A proper subset of a linearly independent set can sometimes form a spanning set. If S is a linearly independent set and T is a spanning set in a vector space V, then SnT is a basis for V. The intersection of two subspaces of a vector space is always a subspace.

A proper subset of a linearly independent set can sometimes form a spanning set. If S is a linearly independent set and T is a spanning set in a vector space V, then SnT is a basis for V. The intersection of two subspaces of a vector space is always a subspace.

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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ONLY 1,2,3

? ? ? ? ? Are the following statements true or false? 1. A proper subset of a linearly independent set can sometimes form a spanning set. 2. If S is a linearly independent set and I is a spanning set in a vector space V, then SnT is a basis for V. 3. The intersection of two subspaces of a vector space is always a subspace. 4. If {u, v, w} is a linearly independent set, then {2u + 3v + 4w, u + 3v, u + 4w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u + 3v, v − 4w, w} is linearly independent.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false? 1. A proper subset of a linearly independent set can sometimes form a spanning set. 2. If S is a linearly independent set and I is a spanning set in a vector space V, then SnT is a basis for V. 3. The intersection of two subspaces of a vector space is always a subspace. 4. If {u, v, w} is a linearly independent set, then {2u + 3v + 4w, u + 3v, u + 4w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u + 3v, v − 4w, w} is linearly independent.
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