One problem related to gasoline engine has been reported for the 2006 Toyota Matrix. The most recently reported issues are listed below.
Twice while driving at 60 mph on the highway (in traffic but not bumper to bumper), my Toyota Matrix engine turned off. I was on the right and able to pull over to the side and restart the engine, however had I been in the left lane this would not have been possible and a serious accident could have happened. The vehicle subsequently was inspected by the dealers' service department (russell Toyota in catonsville, maryland). They could not duplicate the failure and found nothing wrong with the car. The car is only a few months old and has 11,800 miles on it, and has received all proper service checks, oil changes, etc.