Is the set of all pairs of real numbers of the form (0, y), with the standard operations on R2, a vector space? Answer Choices: A) Yes, the set is closed under addition and scalar multiplication so the set is a vector space. B) Yes, all ten vector space axioms hold so the set is a vector space. C) No, the set is not closed under addition. D) No, the set is not closed under scalar multiplication.

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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.