1. Consider the matrix n x n A = a) Calculate the eigenvalues of the triangular matrix A; hence show that the eigenvalues of the triangular matrix A are its diagonal entries. b) For each eigenvalue A determine the number of independent eigenvectors that can share the eigenvalue. (The number of independent eigenvectors N of A is given by: N = n - rank(A - XI). Hint: to find the rank of a matrix read the Kreyszig's book Chapter 7 on Linear Algebra: Matrices, Vectors, Determinants. Linear Systems) c) Find all eigenvectors of the matrix and verify your answer against the outputs from b). d) Calculate the determinant of A and show that it is the product of its eigenvalues