(a) Let V be R², and the set of all ordered pairs (x, y) of real numbers. Define an addition by (a, b) + (c,d) = (a + c, 1) for all (a, b) and (c,d) in V. Define a scalar multiplication by k · (a, b) = (ka, b) for all k € R and (a, b) in V. . Verify the following axioms: (i) k(u + v) = ku + kv (ii) u + (-u) = 0

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question
(a) Let V be R², and the set of all ordered pairs (x, y) of real numbers.
Define an addition by (a, b) + (c,d) = (a + c, 1) for all (a, b) and (c,d) in V.
Define a scalar multiplication by k · (a, b) = (ka, b) for all k E R and (a, b) in V.
.
Verify the following axioms:
(i) k(u + v) = ku + kv
(ii) u + (-u) = 0
Transcribed Image Text:(a) Let V be R², and the set of all ordered pairs (x, y) of real numbers. Define an addition by (a, b) + (c,d) = (a + c, 1) for all (a, b) and (c,d) in V. Define a scalar multiplication by k · (a, b) = (ka, b) for all k E R and (a, b) in V. . Verify the following axioms: (i) k(u + v) = ku + kv (ii) u + (-u) = 0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education