Let V be any vector space. Let c be in R and x be in V. Prove the following. (a) If c0 and cx = 0, then x 0. = (1) (b) If x = 0 and cx = 0, then c = 0. Prof in class. Hint suppose u is not zero. the point is to show that k is zero. Let's pregame that k isn't zero what does that tell us about you? You'll reach a contradiction so it's not possible to have k not zero so k must be zero le

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
icon
Related questions
Question
Let V be any vector space. Let c be in R and x be in V. Prove the following.
(a) If c0 and cx
=
0, then x 0.
=
(1)
(b) If x = 0 and cx = 0, then c = 0.
Prof in class.
Hint suppose u is not zero. the point is to show that k is zero. Let's
pregame that k isn't zero what does that tell us about you? You'll reach a
contradiction so it's not possible to have k not zero so k must be zero
le
Transcribed Image Text:Let V be any vector space. Let c be in R and x be in V. Prove the following. (a) If c0 and cx = 0, then x 0. = (1) (b) If x = 0 and cx = 0, then c = 0. Prof in class. Hint suppose u is not zero. the point is to show that k is zero. Let's pregame that k isn't zero what does that tell us about you? You'll reach a contradiction so it's not possible to have k not zero so k must be zero le
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning