One problem related to engine clicking and tapping noises has been reported for the 2003 Toyota Matrix. The most recently reported issues are listed below.
My son was driving our 2003 Toyota matix, accelerating up to speed after pulling onto the interstate on-ramp when the engine began to make a loud clicking sound. There was no engine warning light or smoking from the engine or exhaust system. He reduced speed, pulled over and exited at the next exit. Although the car had lost significant power, he was able to continue to drive to the dealership, located nearby. The oil pressure switch had failed and the oil had leaked out. There was no level on the dipstick. After replacing the switch, adding oil, the engine still has a loud knocking sound, is low on power and will not idle. It is not burning oil. Diagnosis is internal engine damage and that engine must be replaced. The car has 129,000 miles on it, has been regularly maintained at the dealership and was one month and 1500 miles short of its next oil change. Dealer verbal estimate is $5000 for replacement engine, from a breaker's yard. Independent estimate is $3000 - 4000. Basically, the car is an economic write-off.