How to solve these 2 different questions?

1.

(3 marks) Consider the following matrices: 5 4i H A = E = 4i 5 = ( 9 ) , C = (4 ), D= N. 5 3 The matrices that have real eigenvalues are (select all that apply) OA B OC OD OE The matrices that have non-real eigenvalues that occur in conjugate pairs are (select all that apply) OA OB OC OD OE And finally the matrices that are diagonalisable are (select all that apply) OA OB OC OD OE(3 marks) Let M be a square matrix. For the following statements, either show that the statement is true by providing a proof including all your reasoning, or show the statement is false using an appropriate counter example. i) M and MT have the same eigenvalues. Words: 0 A ii) M and M- have the same eigenvectors. A . A- Ix BIUSX X= ICE Words: 0