Let V be a general vector space and u, v € V be linearly independent. (a) Show that the vectors x = a₁u+a₂v and y = azu+α4v with α; € R are linearly independent if and only if a1a4-a2030. (b) For the case α₁04-a2030, are the vectors {u, v, x, y} linearly independent?
Let V be a general vector space and u, v € V be linearly independent. (a) Show that the vectors x = a₁u+a₂v and y = azu+α4v with α; € R are linearly independent if and only if a1a4-a2030. (b) For the case α₁04-a2030, are the vectors {u, v, x, y} linearly independent?
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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![4. Let V be a general vector space and u, v E V be linearly independent.
(a) Show that the vectors x = a₁u+a₂v and y = azu+a4v with a; E R are linearly
independent if and only if a₁04 - α203 0.
(b) For the case α₁04 - α203 0, are the vectors {u, v, x, y} linearly independent?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F882ce437-6984-48a2-b1c1-0c70a26630a5%2F3bd24223-ae19-4f66-9a38-47256a3b8a25%2Farn7fu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let V be a general vector space and u, v E V be linearly independent.
(a) Show that the vectors x = a₁u+a₂v and y = azu+a4v with a; E R are linearly
independent if and only if a₁04 - α203 0.
(b) For the case α₁04 - α203 0, are the vectors {u, v, x, y} linearly independent?
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