Math 451 Exam 2 Preparation

The exam will include doing some matrix computations by hand and analyzing some codes that do things with matrices. You can bring in one 3"x5" index card with notes on both sides.

Here are the computations that you should be able to perform:

• Row-Reduction Row-reduce a matrix to upper triangular form in the manner we've been doing, and that we've used to code row reduction. Here is a video showing the process.


• Back-Substitution and forward-substitution to solve a system whose coefficient matrix has been put in upper triangular or lower triangular form. These can be seen as part of the video on solving with an LU-factorization.


• LU-Decomposition Determine the matrices L and U for a given square matrix A. Here is a video showing how to do that.


• Solving With an LU-Factorization Given the LU-factorization of a coefficient matrix, solve the associated system of equations. This is demonstrated here


• Iterative Solution Methods Solve a system using the Jacobi or Gauss-Seidel method. Videos here and here.


• Error Determine the error vector and error for a solution to a system of equations as discussed here.

Here are a few practice problems with solutions.

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