Citing law enforcement sources it did not name, the Los Angeles Times reported Saturday Zawahri was apparently angered by his parents' divorce.
The sources said Zawahri's first alleged victims were his father and brother, whose bodies were found Friday in a burning home not far from Santa Monica College, owned by Samir Zawhawi, 55.
The suspect in the subsequent shooting spree -- which ended when police killed him in an exchange of gunfire in the school library -- had been hospitalized for an undetermined amount of time, CNN reported Saturday, citing law enforcement sources close to the investigation. It was unclear whether the suspect committed himself voluntarily, or whether his family or the state had him hospitalized.
CNN said the man was hospitalized "a couple of years ago" for talking about hurting someone.
Laura Sisk of Santa Monica told the Los Angeles Times the gunman carjacked her and forced her to do the drive to the school.
Sisk said she thought for a moment the masked man pointing an assault rifle at her in the middle of the street might be a Secret Service agent assigned to President Barack Obama's visit to Southern California, but she quickly realized otherwise.
Sisk told the Times the gunman told her, "You are going to drive me to Santa Monica College and let me out."
She pleaded to take the car and let her go, but her responded: "No. You're driving."
At one point, the man shot out the windows of a passing bus and told Sisk to "Go! Go! Go!."
"So I drove, drove, drove," she said.
Sisk was released unharmed as promised but the suspect allegedly killed four people and wounded five others before police killed him.
The suspect's identity was not officially released Saturday but the Times said he was believed to the son of a man whose body was discovered inside the burning house.
The FBI Saturday had joined the investigation to help dig into the suspect's background and learn how he obtained the AR-15 assault rifle used in the rampage, law enforcement sources told the Times.
Police have identified one of the victims as Carlos Navarro Franco, 68. Franco lives near the campus and was driving his SUV in the area when the suspect opened fire, CNN said.