6. Suppose that V is a vector space over a field F and that v1, v2, ..., Vn € V. For each statement below, decide if the statement is true. If you believe it is true give a proof; if not, give an example that contradicts the statement. a. If v1, v2, ..., Vn are linearly independent then v1, v2, ... , Un is a basis of V. b. If vi E (v2, v3, ..., Vn) then v1, V2, ... , Vn are linearly dependent. c. If vi E (v1, V2, V3, . . . , Vn) then v1, v2, ..., Vn are linearly dependent. d. If v1, v2, ..., Vn are linearly independent then (v1, V2, ..., Vn) # (v2, ..., Vn)

6. Suppose that V is a vector space over a field F and that v1, v2, ..., Vn € V. For each statement below, decide if the statement is true. If you believe it is true give a proof; if not, give an example that contradicts the statement. a. If v1, v2, ..., Vn are linearly independent then v1, v2, ... , Un is a basis of V. b. If vi E (v2, v3, ..., Vn) then v1, V2, ... , Vn are linearly dependent. c. If vi E (v1, V2, V3, . . . , Vn) then v1, v2, ..., Vn are linearly dependent. d. If v1, v2, ..., Vn are linearly independent then (v1, V2, ..., Vn) # (v2, ..., Vn)

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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