Let V = {x} be a set consisting of a single real number x with the operations of addition and scalar multiplication defined as Addition : x + x = x, Scalar Multiplication : kx = x, ∀ k ∈ R Is V a vector space? If not, identify all the axioms that fail.

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A: given V is set of ordered pair (a,b) where a,b are real number and field is R

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A: In this question, we want to prove that for a vector space V , 0v=0 for all v in V.

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A: Given, x©y = xy + 5 So,  (x©y)©z  = (xy + 5)©z  = (xy+5)z + 5 = xyz + 5z + 5

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Q: Please solve this question with a good explanation. It is Linear Algebra question.

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A: It is a vector space problem. Here this statement is true

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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.