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