The financial advisor of a prominent non-profit organization strategically placed its funds in three distinct asset classes: a secure savings account yielding 4% per annum, a liquid mutual fund offering a return of 7%, and sovereign bonds yielding an 8% return. After a year of investing, the total interest accrued amounted to $178,000. If the amount invested in sovereign bonds is $300,000 more than twice the amount committed to the mutual fund, determine the exact sum allocated to each investment. The total capital invested across all three assets is $2.5 million. Solve using the Gauss- Jordan elimination method.