format rat;

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

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

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

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

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

A = [2, -5; 1, -2]; % Problem 6

A = [3, -2; 4, -1]; % Problem 7

A = [-1, -1; 0, -1/4]; % Problem 8

A = [3, -4; 1, -1]; % Problem 9

A = [1, 2; -5, -1]; % Problem 10

A = [-1, 0; 0, -1]; % Problem 11

A = [2, -5/2; 9/5, -1]; % Problem 12

A = [1, 1; 1, -1]; % Problem 13
A \ [2; 0] 

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

A = [-1, -1; 2, -1]; % Problem 15
A \ [1; -5] 

A = [2, -2.5; 1.8, -1]; % Problem 22

P = [5, 0; 3, -3];
P \ (A * P)

% 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