% create a matrix with prescribed eigenvalues that's easy to solve by hand

% eigenvalues 
		l1 = 1;
		l2 = 2;
		l3 = -3;

% characteristic poly
		syms x
		eqn = expand((x-l1)*(x-l2)*(x-l3));
		cfs = coeffs(eqn);
		c = cfs(1);
		b = cfs(2);
		a = cfs(3);

% build matrix ala Dan Rowe
		M = double([0 0 -c; 1 0 -b; 0 1 -a]);

% create an element of GLnZ as conjugator
		I = eye(3);
		T = I;
		
		for j = 1:3;
			k = randi(3);
			E{j} = T*T;
			T(mod(k,3)+1,:) = (-1)^randi(2)*randi(3)*I(k,:) + I(mod(k,3)+1,:);
		end

		B = E{3};

% conjugate clean matrix by elementary one to hide values and make computation more interesting
		A = B*M*inv(B)
