One problem related to vehicle shudder has been reported for the 2004 Toyota Matrix. The most recently reported issues are listed below.
Low noise from engine area, then heard a pop or thud. After this came a scratchy/grinding noise when car was in gear and coasting. The noise went away when clutch was depressed or car was taken out of gear to coast. I called a service repair to make an appointment the same day. The very next day the car locked up and was undriveable. Sounded like the engine had fallen out the bottom with horrible metal grinding noise. I had to have it towed ($150) and the service center said I would need a new transmission and clutch and that this is a common problem with Toyota Matrix and corolla. After reading online, it seems there is a problem with Toyota owners with low miles having bearing issues and that this problem has gone unaddressed. Even though I was going only 10 miles per hour, the car locks up. This issue will kill someone, someday. Cost of repair will be around $3,100+.