Lead in the Body

Part 2: The Matrix-Vector Formulation

The compartment model

leads to a vector differential equation of the form

where A is the matrix

and b = (L,0,0)^T.

1. Explain carefully each of the entries in A.
2. Explain carefully each of the entries in b.
3. Show that the matrix A is nonsingular. (You may use your helper application.)
4. Find the equilibrium solution x_e of x' = Ax + b, and check your answer.