Abstract
When solving a linear system of equations with a changing righthand side, the bulk of the work can be done by factoring the system's matrix into the product of an upper and lower triangular matrix. This factorization, called LU factorization, allows one to obtain the solution to the system through a forward and backward substitution. The work to obtain the LU factorization is the same as Gaussian elimination, and the need for pivoting is the same. Finally, we discuss the types of matrices that arise in engineering calculations and their common structures.
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