Let V be a finite dimensional vector space. Let T E L(V). (a) Show that there exists an integer n such that Ker(T") = Ker(T+1) = Ker(T"+2) Hint: Ker(Tk) C Ker(T*+1) ... (b) Show that V = Ker(T") Im(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.