Let V be a finite dimensional vector space, and T:        V------->V be a linear operator. Let NT denote the nullspace of T.  Prove that T is invertible iff NT= {0}.

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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.