Given the matrix B = [3 8 -4 0 -1 0 2 4 -3]. (i) Find all the eigenvalues of B. (ii) Find the corresponding eigenvectors of B. (iii) Diagonalize matrix B. (iv) Using the results of (i)-(iii) find B^2013. (b) Consider the following Linear Programming problem: Find values of x and y which maximize z = 5x + 6y subject to constraints: x + y lessthanorequalto 6, 2x + y lessthanorequalto 10, 3x + y greaterthanorequalto 3, where x, y are non-negative numbers. (i) Sketch the set of feasible solutions. (ii) Find the extreme points of the set of feasible solutions. (iii) Find the optimal solution.
Show transcribed image textGiven the matrix B = [3 8 -4 0 -1 0 2 4 -3]. (i) Find all the eigenvalues of B. (ii) Find the corresponding eigenvectors of B. (iii) Diagonalize matrix B. (iv) Using the results of (i)-(iii) find B^2013. (b) Consider the following Linear Programming problem: Find values of x and y which maximize z = 5x + 6y subject to constraints: x + y lessthanorequalto 6, 2x + y lessthanorequalto 10, 3x + y greaterthanorequalto 3, where x, y are non-negative numbers. (i) Sketch the set of feasible solutions. (ii) Find the extreme points of the set of feasible solutions. (iii) Find the optimal solution.