Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over R with addition and scalar multiplication defined by: (i) (a, b) + (c,d) = (a +d,b+c) and k(a, b) = (ka, kb), (ii) (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (a, b), (a, b) + (c,d) = (0,0) and k(a, b) = (ka, kb), (a, b) + (c,d) = (ac, bd) and k(a, b) = (ka, kb). (iii) (iv)

3. Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over R with addition and scalar multiplication defined by: (i) (a, b) + (c,d) = (a +d,b+c) and k(a, b) = (ka, kb), (ii) (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (a, b), (a, b) + (c,d) = (0,0) and k(a, b) = (ka, kb), (a, b) + (c,d) = (ac, bd) and k(a, b) = (ka, kb). (iii) (iv)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 16EQ
See similar textbooks
icon
Related questions
Question
3. Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over R with addition and scalar multiplication defined by: (i) (a, b) + (c,d) = (a +d, b+c) and k(a, b) = (ka, kb), (ii) (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (a, b), (iii) (a, b) + (c,d) = (0,0) and k(a, b) = (ka, kb), (iv) (a, b) + (c,d) = (ac, bd) and k(a, b) = (ka, kb).
Transcribed Image Text:3. Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over R with addition and scalar multiplication defined by: (i) (a, b) + (c,d) = (a +d, b+c) and k(a, b) = (ka, kb), (ii) (a, b) + (c,d) = (a + c,b+d) and k(a, b) = (a, b), (iii) (a, b) + (c,d) = (0,0) and k(a, b) = (ka, kb), (iv) (a, b) + (c,d) = (ac, bd) and k(a, b) = (ka, kb).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 28 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
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
SEE MORE TEXTBOOKS