Hello, I have linear algebra questions.

I need your help.

Thank you so much.

1. Suppose TEL(V) where V is a finite-dimensional complex vector space, and suppose that all the entries of the matrix M(T) with respect to some basis, are real. Prove that if A E C is an eigenvalue of T then so is 1. [10] 2. Suppose T E L(V) is diagonalizable. Prove that V = null(T) @ range(T). Is the converse true? Prove or give a counterexample. [10]