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.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.7: Portfolio Optimization Models
Problem 35P
icon
Related questions
Question
do fast all
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
Practical Management Science
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,