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The Matrix already has fairly compliant suspension as it is - you could run a softer spring, but with such a large sail area, you are trading ride compliance for overall vehicle handling. IMO, that is a poor trade-off. Sure you'd soften the ride, but get a good cross-wind gust, and you might find yourself immediately punched over another lane.
Assuming that you've already looked at the tire pressures - made sure they are not too high. Also made sure there was no physcial issue preventing the suspension to do its job (i.e., frozen coil or strut by ice jammed in there).
A more reliable and safer way to approach the ride are to adjust tire pressures (to a certain extent) or consider upgrading to a touring type of tire. Those have unique tire carcass that designed for a smoother, quieter ride while maintaining enough structural stiffness to provide good handling and stability. Tire pressures listed by the OEM may not be applicable for your driving conditions. Those numbers are generated to work in a wide range of conditions, but you may find that you'll have to run more or less pressure in the rear axle to compensate for the overall ride. Having that beam axle in the back will not help, but the right tire pressure and the right tire will make a huge difference in the car's handling and ride.
The OEM All-Season Goodyears on my Matrix were OK tires, but when I replaced them with dedicated summer tire for most of the year (have winter tires mounted separately on a spare set of wheels) - the ride was vastly transformed. Not Lexus smooth, but handled pavement irregularities much better than the OEM Goodyears. Now I "hear" the pavement cracks and whatnot instead of "feeling" them.
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2002 Corolla S, 1.8L 1ZZ-FE VVT-i
2003 Matrix XRS, 1.8L 2ZZ-GE, VVTL-i (RIP)
2009 Matrix XRS, 2.4L 2AZ-FE VVT-i
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