format rat;

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

A = [-3/4, 1/2; 1/8, -3/4]; % Problem 2

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

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

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

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

A = [5, -1; 3, 1]; % Problem 7

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

A = [1, 1, 1; 2, 1, -1; -8, -5, -3]; % Problem 9

A = [1, -1, 4; 3, 2, -1; 2, 1, -1]; % Problem 10

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

A = [-1, -4; 1, -1]; % Problem 12

% 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