2003 Chevy Malibu car shakes

Could be one of several things:

Have tires balanced and 4 wheel alignment.

Inspect brake rotors for an out of round condition. While a dial indicator is best, you can remove rotor and lay on flat surface, should lay flat, if any wobble, replace rotors and inspect pads for wear.
Also make sure the calipers are not stuck and there are no brake fluid leaks.

Finally, raise car put on stands, grasp wheel and push/pull with both hands on outside of tire. You are looking for any movement. If movement, then inspect hub bearings, tie rod ends, control arm and bushings.

I would suspect an alignment/tire issue with a car this new, as opposed to a suspension component.

thanx, because i was thinking it was an issue with the engine.

Thanks for using 2carpros.