Problem$-2$:

A$)$ Determine the stoichiometric matrix for the network with two additional reactions: production of $S,$ with rate $v_0,$ and consumption of $P,$ with rate $v_4.$

B$)$ By addressing the rows of $N,$ verify that, in this case the total enzyme is still conserved, but there is no conservation involving $S$ or $P.$ correspond to the two conservations, lie in the kernel of the transpose of $N.$