Solve the following word problem using matrices: Part of $30,000 is invested at 6% yearly interest, another part at 7%, and the remainder at 8% yearly interest. The total yearly interest income from the three investments adds up to $2200. The sum of the amounts invested at 6% and 7% equals the amount of money invested at 8%. How much is invested at each rate?

(Enter your answer in the form $x, xxx--with the amount invested at 6% first, then 7%, then 8%.)