Let W = {A € M3x3(R) : A" = -A}. (a) Prove that W is a subspace of V = M3×3(R). (b) Construct a basis for W and prove that your proposed set is, in fact, a basis. Compute the dimension of W (Hint: The entries along the main diagonal should be 0, by a previous quiz problem.)

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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.