Let T : V → V be a linear operator over a finite dimensional vector space V . Prove that dim(ker(T)) + dim(ImmT) = Dim(V ). b) Give an example of a linear operator T : V → V over a finite dimensional vector space V . such that ker(T)⊕ImmT / 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.