Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations: Vector addition: a + b - ab, where a, b are real numbers not including -1 Scalar Multiplication: c· a = 0 where a is a real number not including -1 and c is a scalar

Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations: Vector addition: a + b - ab, where a, b are real numbers not including -1 Scalar Multiplication: c· a = 0 where a is a real number not including -1 and c is a scalar

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

S is not a vector space. List all vector addition properties that fail to hold (at least 2). List all scalar multiplication properties that fail to hold (at least 2).

Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations:
Vector addition: a + b - ab, where a, b are real numbers not including -1
Scalar Multiplication: c· a = 0 where a is a real number not including -1 and c is a scalar

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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