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Let V be a vector space, and let x,y be distinct elements of V (i.e. xy. (a) Prove that if x is a scalar multiple of y, then the set {x,y) is linearly dependent. (b) Prove that if {x,y} is linearly dependent, then either x is a scalar multiple of y ory is a scalar multiple of x. (c) Prove that {x,y} is linearly independent if and only if {x-y,x + 2y} is linearly independent.

Let V be a vector space, and let x,y be distinct elements of V (i.e. xy. (a) Prove that if x is a scalar multiple of y, then the set {x,y) is linearly dependent. (b) Prove that if {x,y} is linearly dependent, then either x is a scalar multiple of y ory is a scalar multiple of x. (c) Prove that {x,y} is linearly independent if and only if {x-y,x + 2y} is linearly independent.

Understanding Business
Understanding Business
12th Edition
ISBN:9781259929434
Author:William Nickels
Publisher:William Nickels
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
Section: Chapter Questions
Problem 1CE
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Let V be a vector space, and let x,y be distinct elements of V (i.e. xy. (a) Prove that if x is a scalar multiple of y, then the set {x,y) is linearly dependent. (b) Prove that if {x,y} is linearly dependent, then either x is a scalar multiple of y ory is a scalar multiple of x. (c) Prove that {x,y} is linearly independent if and only if {x-y,x + 2y} is linearly independent.
Transcribed Image Text:Let V be a vector space, and let x,y be distinct elements of V (i.e. xy. (a) Prove that if x is a scalar multiple of y, then the set {x,y) is linearly dependent. (b) Prove that if {x,y} is linearly dependent, then either x is a scalar multiple of y ory is a scalar multiple of x. (c) Prove that {x,y} is linearly independent if and only if {x-y,x + 2y} is linearly independent.
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