Let V be a finite dimensional vector space and T: V V be linear. A subspace WCV is T-invariant if T (W) CW. (a) Prove that the subspaces {0v}, V, R(T), and N (T) are T-invariant. (b) Suppose V = R (T) W where W is T-invariant. Prove that W = N (T).

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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.