2. Consider the mixing process shown below, where the indicated compositions of A, B, and C are mass fractions G 0.50 A 0.50 C F H 0.10 A 0.20 B 0.70 C 0.20 A 0.30 B 0.50 C 0.35 A 0.10 B 0.55 C P= 100 kg/hr The following mass balance equations can be derived to describe this system: 0.1F +0.5G +0.2H = 35 0.2F + 0.3H = 10 0.7F + 0.5G + 0.5H = 55 Considering these mass balances, formulate these equations in matrix form. Does this system of equations have a unique non-trivial solution? Justify your answer. If so, solve this linear system of equations using Gaussian elimination. (50 points)