format rat;

A = [2, -1; 3, -2]; % Problem 1

A = [1, sqrt(3); sqrt(3), -1]; % Problem 2

A = [2, -5; 1, -2]; % Problem 3

A = [1, 1; 4, -2]; % Problem 4

A = [4, -2; 8, -4]; % Problem 5

A = [-4, 2; 2, -1]; % Problem 6

A = [1, 1; 4, 1]; % Problem 7

A = [2, -1; 3, -2]; % Problem 8

A = [-5/4, 3/4; 3/4, -5/4]; % Problem 9

A = [-3, sqrt(2); sqrt(2), -2]; % Problem 10

A = [2, -5; 1, -2]; % Problem 11 and 12

A = [-1/2, -1/8; 2, -1/2]; % Problem 13

A = [2, -1; 3, -2]; % Problem 14

A = [3, -2; 2, -2]; % Problem 15

A = [-2, 1; 1, -2]; % Problem 18

% Compute the eigensystem for the matrix A:
%
m = size(A, 1);
e = eig(A)
for ii=1:m
    rref(A - e(ii)*eye(m))
end