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chemical reaction and linear system of equations

If you could hand write the answer I would appreciate it

chemical reaction and linear system of equations Establish a mass balance for alcoholic fermentation, i.e. \[ x_{1} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \quad \rightarrow \quad x_{2} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+x_{3} \mathrm{CO}_{2} \] a) Set up a (quadratic) linear equation system in matrix notation to solve the problem. \[ A \cdot \vec{x}=\vec{b} \] b) Check with the determinant whether the Linear Equation System can be solved uniquely. c) Solve the LES with the Gauss-Jordan algorithm and give a solution for the mass balances. d) Justify that there is no inverse matrix of the coefficient matrix.

a) The mass balance equations for each component must first be written in order to set up a linear equation system for the specified chemical reaction. Given is the mass balance for glucose (C6H12O6): C6H12O6 = x1m(x2m) (C2H5OH) For ethanol (C2H5OH),