Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Show that for any vector v e R°, P(v) is perpendicular to u. 4. Show that if P(v) = 0 then v is a sc alar multiple of u. 5. True or false: any vector v e R³ can be expressed as a sum v = w + w' where w is a scalar multiple of u and w' is perpendicular to u. Does the mapping P relate to this? 6. Suppose v1, v2 are two nonzero vectors perpendicular to u and to each other. What are the values of P on u, v1. 2?

3. Show that for any vector v e R°, P(v) is perpendicular to u. 4. Show that if P(v) = 0 then v is a sc alar multiple of u. 5. True or false: any vector v e R³ can be expressed as a sum v = w + w' where w is a scalar multiple of u and w' is perpendicular to u. Does the mapping P relate to this? 6. Suppose v1, v2 are two nonzero vectors perpendicular to u and to each other. What are the values of P on u, v1. 2?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 6AEXP
See similar textbooks
icon
Related questions
Question

Could you solve parts 4,5,and 6?

Problem 5. Let u be a unit vector in R3 and let P: R³ → R³ be defined by P(v) = v – (v • u)u. 1. Show that P is linear. 2. Show that PoP= P. 1 3. Show that for any vector v e R³, P(v) is perpendicular to u. 4. Show that if P(v) = 0 then v is a scalar multiple of u. 5. True or false: any vector v E R³ can be expressed as a sum v = w + w' where w is a scalar multiple of u and w' is perpendicular to u. Does the mapping P relate to this? 6. Suppose vi, v2 are two nonzero vectors perpendicular to u and to each other. What are the values of P on u, v1, v2?
Transcribed Image Text:Problem 5. Let u be a unit vector in R3 and let P: R³ → R³ be defined by P(v) = v – (v • u)u. 1. Show that P is linear. 2. Show that PoP= P. 1 3. Show that for any vector v e R³, P(v) is perpendicular to u. 4. Show that if P(v) = 0 then v is a scalar multiple of u. 5. True or false: any vector v E R³ can be expressed as a sum v = w + w' where w is a scalar multiple of u and w' is perpendicular to u. Does the mapping P relate to this? 6. Suppose vi, v2 are two nonzero vectors perpendicular to u and to each other. What are the values of P on u, v1, v2?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS