One problem related to transmission shudder has been reported for the 2004 Toyota Matrix. The most recently reported issues are listed below.
Had to replace the transmission on my 2004 Matrix. The car has been making noise for the last several months. I did not take it to the shop to find the noise because it ran fine. The last time I started the car before it broke down the noise was really loud and did not drive very well. The transmission and clutch shifted fine. Car broke down on the interstate. Was able to get off the first exit. Took it the repair shop. They described it as a metal grinding noise and saw heavy vibrations from the transmission when the car was on the lift. Replaced the transmission for $2700. Got the car back, drives fine. No noise.