Consider the following subset W of the given vector spaces V . (i) Find two nonzero (non-trivial) elements in W and justify why they belong to W. (ii) Determine whether W is a subspace of V . Give proof if it is, or a counter example if it is not. V = M_(n×n)(R), W = {A ∈ M_(n×n)(R) | A is symmetric} where R is the set of real numbers. (Recall: A is symmetric if A^T = A)

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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.