format rat;

A = [0, -1; 1, 0]; % Problem 3
[0, 1; 1, 0] \ [4; 0]
[0, 1; 1, 0] \ [0; 4]

A = [0, 1; 2, 1]; % Problem 19

A = [-1, 1; -1, -1]; % Problem 20

% 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