# Math 230 - Chapter 8-9 Study Guide

1. Determine whether the vectors form a fundamental set on (-∞,+∞). Two parts.
2. Verify that the vector X is a solution of the given system. Two parts.
3. Find the general solution of the system. Three parts.
4. Find the general solution of the system. Use REF or RREF on your calculator as needed. Two parts.
5. Use Variation of Parameters to solve. Two parts.
6. Find the Matrix Exponential using the definition
7. Find the Matrix Exponential using Laplace Transforms and then find the General Solution
8. Use the eigenvalues and eigenvectors from Maxima to write the general solution with real coefficients.
9. Use the RK4 method to approximate the given value,

## Notes

• You may need to bring scratch paper for extra work, although most of the problems shouldn't require more space than is given.
• There is no Maxima allowed on this exam. The problems are 2×2 matrices or can be worked out on the calculator. In other cases, the output from Maxima is given on the exam.
• #9 is the take home question for chapter 9. It is due the day of the exam.
• Some time saving formulas for integration and differentiation are given on the exam. You may or may not need them. Do not infer that you have missed something if you do not use one of them.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 Total 6 8 21 14 16 6 7 6 16 100