? Are the following statements true or false? 1. If {u, v, w} is a linearly independent set, then {2u + 2v+6w, u + 2v, u +6w} is linearly independent.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Are the following statements true or false?
1. If {u, v, w} is a linearly independent set, then {2u + 2v+6w, u + 2v, u +6w} is linearly independent.
2. The intersection of two subspaces of a vector space is always a subspace.
✓3. There exist vectors u, v, w ER ³ such that u - v, v - w, w - u span R³
4. A proper subset of a linearly independent set can sometimes form a spanning set.
5. The basis for the zero vector space {0} consists of the zero vector itself.
Transcribed Image Text:? ? ? ? ? Are the following statements true or false? 1. If {u, v, w} is a linearly independent set, then {2u + 2v+6w, u + 2v, u +6w} is linearly independent. 2. The intersection of two subspaces of a vector space is always a subspace. ✓3. There exist vectors u, v, w ER ³ such that u - v, v - w, w - u span R³ 4. A proper subset of a linearly independent set can sometimes form a spanning set. 5. The basis for the zero vector space {0} consists of the zero vector itself.
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