1b.
M=[1 1; 0 1];
M^25

2a.
b=[2;3];
M=[1 1; 0 1];
M*b %works
b*M %does not work

2b.
b'*M
M*b'

%M has 2 columns, but b' has only 1 row.

3.
function out = diffeqn(in, sigma, omega)
M = sigma*[cos(omega), -sin(omega); sin(omega), cos(omega)];%given
b = [0;1];%given
c = sigma*[-cos(omega); sin(omega)];%given
%zero response, so intial state is 0
state = [0;0];%given
for i=1:length(in)
	out(i) = c'*state;
	state = M*state + b*in(i);
end




path(path, 'U:\Lab05\InLab\');
in = [1, zeros(1,99)];
subplot(3,1,1); plot(diffeqn(in, 1, pi/8));
subplot(3,1,2); plot(diffeqn(in, 0.95, pi/8));
subplot(3,1,3); plot(diffeqn(in, 1.05, pi/8));

%sinusoid when sigma =1
%others are sinusoidal x exponential. 

%3d. sigmaa=1 is periodic with period of 16 samples
%3e. sigma =0.95 is stable, and sigma=1.05 is unstable. Sigma =1 is oscillating.