Prove that a nonempty subset U of a vector space Vover a field F is a subspace of V if, for every u and u' in U and everya in F, u + u' ∈ U and au ∈U. (In words, a nonempty set U isa subspace of V if it is closed under the two operations of V.)

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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.