A closed-system 3-box model with concentrations as the variables

1 A closed-system 3-box model with concentrations as the variables 

These three equations are not independent which can be checked by adding all three 

Dividing each equation by the volume of the corresponding reservoir, we get 

The matrix is singular since Vx multiplied by the first line + V2 multiplied by the second line + V3 multiplied by the third line sums up to zero. 

An entirely equivalent formulation uses the absolute amounts FjC, present in each reservoir instead of concentrations 

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