Upon claiming a $350,000 inheritance from a distant relative, famed musician Oliver resolved to distribute this unanticipated fortune into three distinct investments: a time deposit offering a 3.5% return, a municipal bond yielding 4.5%, and a mutual fund yielding 6.5%. After one fiscal year, his investment portfolio garnered a notable $17,500 in earned interest. Determine the amount Oliver allocated to each investment, knowing that he invested $25,000 more into the mutual fund than he did in the municipal bond. Utilize a matrix method of solving systems of equations to find the solution