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3. Show that if two vectors in the set {a1, a2,... , ak} are identical, then the set is linearly dependent. 4. Show that if a set S is linearly independent in a vector space V over F, then every nonempty subset of S is linearly independent in V.

3. Show that if two vectors in the set {a1, a2,... , ak} are identical, then the set is linearly dependent. 4. Show that if a set S is linearly independent in a vector space V over F, then every nonempty subset of S is linearly independent in V.

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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please prove 3 and 4
3. Show that if two vectors in the set {a1, a2,... , ak} are identical, then the set is linearly dependent. 4. Show that if a set S is linearly independent in a vector space V over F, then every nonempty subset of S is linearly independent in V.
Transcribed Image Text:3. Show that if two vectors in the set {a1, a2,... , ak} are identical, then the set is linearly dependent. 4. Show that if a set S is linearly independent in a vector space V over F, then every nonempty subset of S is linearly independent in V.
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