Determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails.The set of all first-degree polynomial functions ax + b a, b ≠ 0, whose graphs do not pass through the origin

Determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails.The set of all first-degree polynomial functions ax + b a, b ≠ 0, whose graphs do not pass through the origin

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 17E: Testing for a Vector Space In Exercises 13-36, determine whether the set, together with the standard...

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails.
The set of all first-degree polynomial functions ax + b a, b ≠ 0, whose graphs do not pass through the origin

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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