format rat;

A = [3, -4; 1, -1]; % Problem 1

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

A = [-3/2, 1; -1/4, -1/2]; % Problem 3

A = [-3, 5/2; -5/2, 2]; % Problem 4

A = [1, 1, 1; 2, 1, -1; 0, -1, 1]; % Problem 5

A = [0, 1, 1; 1, 0, 1; 1, 1, 0]; % Problem 6

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

A = [-5/2, 3/2; -3/2, 1/2]; % Problem 8

A = [2, 3/2; -3/2, -1]; % Problem 9

A = [3, 9; -1, -3]; % Problem 10

A = [1, 0, 0; -4, 1, 0; 3, 6, 2]; % Problem 11

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

A = [3, -4; 1, -1]; % Problem 13

A = [1, -4; 4, -7]; % Problem 14

A = [1, -1; 1, 3]; % Problem 17

A = [1, 1, 1; 2, 1, -1; -3, 2, 4]; % Problem 18

A = [5, -3, -2; 8, -5, -4; -4, 3, 3]; % Problem 19

% 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