1) Find the eigenvectors and eigenvalues of the matrix A. Hence find the matrix P and a diagonal matrix D such that A = P^?1 DP and compute A^100 (see attached).
2.i) Verify the Cayley-Hamilton theorem for the matrix A.
ii) Compute the minimal polynomial of a matrix A and decide whether the matrix is diagonalizable or not. The same question for the matrix B (see attached).
We solve several problems in linear algebra.