Are the following statements true or false? 1. There exist vectors u, v, w R³ such that u V, V-W, W u span R³ 2. If S x wl is a linearly independent set then £2, +5+6w w+ 5x + 6url is lir

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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Are the following statements true or false?
1. There exist vectors u, v, w e R' such that u
v, v – w, w – u span R
?
2. If {u, v, w} is a linearly independent set, then {2u + 5v + 6w, u+ 5v, u + 6w} is linearly independent.
?
3. A subset of a spanning set can sometimes form a linearly independent set.
Transcribed Image Text:Are the following statements true or false? 1. There exist vectors u, v, w e R' such that u v, v – w, w – u span R ? 2. If {u, v, w} is a linearly independent set, then {2u + 5v + 6w, u+ 5v, u + 6w} is linearly independent. ? 3. A subset of a spanning set can sometimes form a linearly independent set.
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