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= 7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' {ku, v} is also a basis for V for every nonzero scalar k. (Hint: You must prove that B'is linearly independent and that it spans V).

= 7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' {ku, v} is also a basis for V for every nonzero scalar k. (Hint: You must prove that B'is linearly independent and that it spans V).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
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7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' = {ku, v} is also a basis for V for every nonzero scalar k. (Hint: You must prove that B'is linearly independent and that it spans V).
Transcribed Image Text:7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' = {ku, v} is also a basis for V for every nonzero scalar k. (Hint: You must prove that B'is linearly independent and that it spans V).
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