At first glance, this is a somewhat mismatched system. But not necessarily. More detail is required.
A 2000W inverter is somewhat oversized for a single 100Ah battery (with max discharge of 100A, and reccomended discharge of ~20-50 for longevity). A full 2000W would be in the ballpark of 180A, but of course, just because you have a 2000W inverter doesn't mean you ever need to use the max power available, a little overhead isn't a bad thing.
A ratio of 100W of solar to 1280Wh battery is pretty anemic on the solar side. It would take multiple days of good sun to fully recharge the battery. But the variable that makes a bigger difference is your daily usage. If you only plan to use 10% or 20% of the battery capacity per day, 100W might be plenty. Additionally alternative charge sources matter, you mention alternator charging, if this is your primary recharge method, and solar is just a supplement, 100W might be fine. Determining how much you expect to use in an average day and in a 'worst case' day will help you work the rest out.
note: if you do want to charge via the alternator, you will need a DC-DC charger designed for charging lifepo4 from a vehicle alternator. Victron, Renogy, Kisea are a few of the companies that make these.