The metabolites A and B are produced and consumed by four reactions. The rates of the reactions are the unknwons r1,r2,r3,r4. It is convenient to think of the four individual rates as entries in a four-dimensinoal flux vector r={r1,r2,r2,r4}. The connectivify of the network is captured by a stoichiometric matrix S : S=1010110101110111 Conservation of mass requires that Sr=0. This homogeneous system has the trivial solution r=0, however. we would like to find more interesting. non-trivial solution- a) Using elementary row operations, calculate the rank of S. Show the row echelon form of S. cPlace answer heres b) Find a parameterized solution for the system Sr=0. liace answer heres c) Find a specific solution for the system by choosing values for the parameters. Place answer heres d) Explain why you would expect the system to have the rank it does. Your answer should discuss the reaction network and the conservation of mass, not the linear dependence of the rows or columns in S. Hint: how many reaction rates do we need to know to specify the network? Place answer heves