Through monthly deductions from his salary, Noah managed to accumulate $4800 per month last year for his future sabbatical trip. His savings account yielded 4.2% interest, his real estate investment trust (REIT) gained 5.75%, but his commodity portfolio dipped by 2.5%. If his overall profit for the year was $104.50, and he invested $300 more in commodities than in REITs, how much was allocated to each investment category? (Formulate a system of equations and solve it by utilizing the inverse matrix method.)