Let V be the set of all ordered pairs of real numbers with addition defined by (x1, x2) + (y1, y2) = (x1 + y1, x2 + y2) and scalar multiplication defined by α ◦ (x1, x2) = (αx1, x2) Scalar multiplication for this system is defined in an unusual way, and consequently we use the symbol ◦ to avoid confusion with the ordinary scalar multiplication of row vectors. Is V a vector space with these operations? Justify your answer.

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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.