Problem 4. In parts (a) - (e) determine whether the statement is true or false or complete the statement, and justify your answer (a) There is a nilpotent matrix with eigenvalue 1. (b) If A is a nilpotent matrix and A*v / 0, then the vectors V, Av, A'v. . . . , A *v are linearly independent. (c) Let A E C and A be an operator on a finite dimensional space V. A finite sequence {vx}"_, of nonzero vectors in V is called a Jordan Chain of length n if (d) If T is a linear operator on a finite-dimensional vector space V, X e C, and G(X, T) is a generalised eigenspace, then G(), T) = N ((T - X1)dimv ). (e) Which of the following matrices are in the Jordan Normal form? 0 0 0 0 (a) 0 1 0 ( b ) 0 0 (c) 0 0 O 0 0 0 0