2. Use the following figure to construct a model for the number of pounds of salt ₁ (t), ₂(t), and z3(t) at time t in tanks A, B,

and C, respectively. Write the model in matrix form and then solve it using eigenvalue/eigenvector techniques assuming that

21 (0) = 15, 22(0) = 10, and 23 (0) = 5. Will all of the tanks eventually be free of salt? Use your solution to justify your answer.

pure water

4 gal/min

200 gal

mixture

4 gal/min

150 gal

mixture

4 gal/min

امع 1000

mixture

4 gal/min