Here we are given only one component of a magnetic field and find all the other components of a cylindrical symmetric magnetic field.

In this fifth video we cover the lu decomposition, which plays a crucial role in understanding how we can solve a linear system computationally. To do the lu decomposition we utilize the Structured Gaussian Elimination algorithm we discussed in the fourth episode. If you need a refresher here is a link to that video. https://youtu.be/59TAcVWZ0LY The 4th video's repo directories: https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/4_Structured_GE https://gitlab.com/n_space_cowboy/computational-linear-algebra/-/tree/master/4_Structured_GE The lu decomposition is a specific configuration of a matrix decomposition that allows us to show that the solutions to the upper triangular system we get from structured Gaussian elimination satisfy the original linear system Ax=b. We explore the lu decomposition computationally in the octave an python languages, utilizing numpy and scipy. This episodes directory in the series repo can be found in the following links. https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/5_LU_Decomposition https://gitlab.com/n_space_cowboy/computational-linear-algebra/-/tree/master/5_LU_Decomposition Understanding the lu decomposition if also crucial for understanding other matrix decompositions since it is one of the more general matrix decompositions. If you have any comments, questions or concerns feel free to let me know in the comment section.