**Characteristic polynomials, eigenvalues, eigenvectors**

Page 110 Number 7, 9, 20**Homogeneous systems, general solutions, initial value problems**

Page 126 Number 1, 4, 9**Matrix solutions, fundamental matrix**

Page 135 Number 1, 16, 17, 24**Inhomogeneous systems, undetermined coefficients, variation of parameters**

Page 149 Number 6, 7, 9, 10

Page 154 Number 1, 2**Modeling with systems**

Two 100 gallon tanks are initially filled with pure water. Fluid is exchanged between the two tanks through a pair of pipes, through which fluid is pumped in opposite directions at a rate of 5 gallons per minute. At the same time, a brine solution containing 5 pounds of salt per gallon is pumped into tank 1 at a rate of 10 gallons per minute, and pure water is pumped into tank 2 at a rate of 5 gallons per minute. The overflow from each tank is allowed to drain off, so that the volume of fluid in each tank remains constant.- 1.
- Set up a system of differential equations for the amount of salt in each tank.
- 2.
- Solve the system, and use the solution to find the concentration of salt in each tank as the system approaches equilibrium (for large time).