In just about every episode Mathews doesn't need much provocation to waste someone. In this episode the bad guy has killed three women, shot at Mathews and shot at two uniformed officers. They never return fire and actually treat the murderer rather politely. In the previous episode a bad guy with a rifle is killed and Mathews afterwards grabs the "dead" man by the hair and never checks for vitals. I guess he could tell if a person was dead just by doing that. Lt Mathews is not a nice man or a good cop.