# 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?

Math 210-01: Linear Algebra: Reading Homework 7.4