One problem related to vehicle shudder has been reported for the 2003 Toyota Matrix. The most recently reported issues are listed below.
I heard a scraping and grating noise as I exited the freeway that I thought was some trapped debris under the front end or in the wheel well. I pulled into a gas station to investigate, finding a loose plastic plate ( a recurring problem with the cheap plastic screws and fasteners used) I rigged something to hold it up and get home. After a few more blocks the sound intensified and the car began to shudder and shake and I heard a pop. I pulled over, got towed home, and the next morning had it towed to a shop. The mechanic informed me that my transmission was shot and would need to be replaced. The car only has 140,000 miles on it, and I do not drive it like some crazed maniac. An internet chat room has recorded lots of Matrix owners with the same transmission issues. . . I am going to need a new transmission and a new clutch.