argent answered required

Question 3 Consider the matrix -7 A =-6 8 Loo 0 O (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 -4a3 - 24c3 6a3+ 24ca AB3 = -4a3 - 16c3 6a3+ 16c3 0 0 -2763 Compute the eigenvalues of matrix B, in terms of a, b and c, of the corresponding eigenvectors. (16 marks)