Matt was a rookie police officer in Philadelphia and was married to Stacey for an unknown amount of time. Together, they had one daughter, Kaylee Ehrmantraut. Matt was also very close to his father, Mike Ehrmantraut, whom he always admired very much and hoped to one day become a successful police officer just like him. Matt worked with his longtime partner, Officer Hoffman, who one day came to him offering dirty money, which Matt denied, believing it was the right thing to do.
Sergeant Fensky later pressed Matt on taking the money. Confused, Matt called his father to ask what to do. He wanted to go to Internal Affairs and inform against his partner and sergeant. Mike was worried that if Matt ratted out on his work colleagues, this would eventually put him in trouble with the rest of the precinct, which was full of dirty cops just like Hoffman and Fensky. So Mike revealed to his son that he was also a dirty cop and there's nothing wrong with taking dirty money, the bad guys are caught in the end no matter what. Matt put his father on a pedestal before, and this revelation left him devastated. Matt eventually decided to follow his father's advice and took the money. But it was too late, Fensky and Hoffman were scared that Matt would rat them out, so they set up an ambush to kill Matt. This crime since then became a mystery to the city's police department, since no one ever found out who killed Matt ("Five-O").
Better Call Saul
It is revealed through flashback that after months of investigation, Mike was able to put the pieces together and discovered that it was Hoffman and Fensky who killed his son. So he was able to set up a similar ambush to kill both police officers and avenge his son's death.
Detectives from Philadelphia later visited Mike in his new home in Albuquerque to question him about the deaths of Hoffman and Fensky, since their death scene was pretty similar to Matt's death scene, and Mike curiously left the State the day after the two died. With some help from his lawyer, Jimmy McGill, Mike is able to evade any questions and gets out of the situation. He later has a conversation with his daughter-in-law, Stacey, revealing that he feels extremely guilty and upset about Matt's death ("Five-O").