Math 210-01: Linear Algebra: Reading Homework 7.4

1. Applications of Eigenvalues and Eigenvectors :
   
   1. Population Growth : how are vectors used to represent populations? what is an age transition matrix?
      
      1. eigenvalues : how do we encounter an eigenvalue problem in this case?
         
   2. Differential Equations : what is a system of linear differential equations?
      
      1. solutions : what solutions does the book find for the system of differential equations in example 3?
         
      2. types of systems : for what types of coefficient matrices will the system y' = A y have simply obtained solutions like this?
         
      3. eigenvalues : how do the types of eigenvalues of the coefficient matrix influence the solutions to the system?
         
   3. Quadratic Forms : how can eigenvalues and eigenvectors be used to work with quadratic forms? how is the matrix of a quadratic form written?
      
      1. matrices : how can a general quadratic expression be written using the matrix of the quadratic form?
         
      2. diagonalization : how is diagonalization related to the rotation of quadratic forms?