Consider the matrix A=⎣⎡−7−6098000−1⎦⎤ (a) Show, with working, that the eigenvalues of A are −1 and 2 . (6 marks) (b) Calculate the eigenvectors of the corresponding eigenvalues. (8 marks) (c) Suppose that a matrix B is diagonalizable and shares the same eigenvectors as matrix A. Given that AB3=⎣⎡−4a3−24c3−4a3−16c306a3+24c36a3+16c3000−27b3⎦⎤ where a,b and c are real constants, compute the cigenvalues of matrix B, in terms of a,b and c, of the corresponding cigenvectors
