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1. 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. 2. The basis for the zero vector space {0} consists of the zero vector itself. 3. There exist vectors u, v, w€ R³ such that u - v, v - w, w - u span R³ 4. If {u, v, w} is a linearly independent set, then {2u +3v + 3w, u + 3v, u + 3w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u+ 3v, v - 3w, w} is linearly independent.

1. 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. 2. The basis for the zero vector space {0} consists of the zero vector itself. 3. There exist vectors u, v, w€ R³ such that u - v, v - w, w - u span R³ 4. If {u, v, w} is a linearly independent set, then {2u +3v + 3w, u + 3v, u + 3w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u+ 3v, v - 3w, w} 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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? ? ? ? ? v 1. 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. 2. The basis for the zero vector space {0} consists of the zero vector itself. 3. There exist vectors u, v, w€ R³ such that u v, v - w, w - u span R³ 4. If {u, v, w} is a linearly independent set, then {2u +3v + 3w, u + 3v, u +3w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u+ 3v, v − 3w, w} is linearly independent.
Transcribed Image Text:? ? ? ? ? v 1. 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. 2. The basis for the zero vector space {0} consists of the zero vector itself. 3. There exist vectors u, v, w€ R³ such that u v, v - w, w - u span R³ 4. If {u, v, w} is a linearly independent set, then {2u +3v + 3w, u + 3v, u +3w} is linearly independent. 5. If {u, v, w} is a linearly independent set, then {u+ 3v, v − 3w, w} is linearly independent.
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