Is there more than one Q-matrix update formula? I asked a question a while ago here and since then I've been solving the issues within my code but I have just one question... This is the formula for updating the Q-Matrix in Q-Learning:

$$Q(s_t, a_t) = Q(s_t, a_t) + \alpha \times (R+Q(s_{t+1}, max_a)-Q(s_t, a_t))$$

However, I saw a Q-Learning example that uses a different formula, which I'm applying to my own problem and I'm getting good results:

$$Q(s_t, a_t) = R(s_t,a_t) + \alpha \times Q(s_{t+1}, max_a)$$

Is this valid?
No, your second statement does not correctly implement the Q-learning update rule, which the first statement correctly implements.