How can Bob decrypt the message?
Bob just needs to multiply the inverse "secret matrix (sm)" to the encrypted message.
Can Eve decrypt the message without finding the inverse of the secret matrix?
YES, by asking Alice what the secret matrix is.
What is the decrypted message corresponding to (2,23,3)?
We go to an enineer-in-training's favorite program Matlab and
We let the decrypted message, es = [1 0 4; 0 1 0; 1 0 1];
We let the encrypted message, ds = [2 0 0; 0 1 0; 0 0 3];
so that (sm)(es) = ds which in matlab means sm = ds*inv(es)
sm = [-2/3 0 2/3; 0 1 0; 4 0 -1]
and now we have a newds=[2; 23; 3]
newes = inv(sm)*newds = [2;23;5]
The letters are BWS.
