Gaussian Elimination

matqkks

I would normally use Gaussian ELimination to solve a linear system. If we have more unknowns than equations we end up with an infinite number of solutions. Are there any real life applications of these infinite solutions? I can think of solving puzzles like Sudoku but are there others?

chiro

Hey matqkks.

Have you ever studied eigenvector/eigenvalue problems?

matqkks

Yes but that comes much later. I am really looking for a real life application outside of its use in linear algebra.

HallsofIvy

Back in the mid twentieth century, the United States Department of the interior did a project to "normalize" township boundaries. Because they were all surveyed at different times, by different people, and with different quality equipment, such boundaries often did not match up and the errors can accumulate to quite sizeable errors.

Rather than re-survey the entire United States (well, actually, just the 48 "contiguous" states) it was decided to use a computer to shift boundaries to minimize the errors. I don't remember the exact numbers but there were something like 300,000 equations with 250,000 variables. That would, of course, result in 50,000 "slack variables" which were set using a "relaxation" technique.

AlephZero

One application is analysing a mechanical device that contains moving parts, like a robot arm. The "infinte solutions" correspond to the ways the arm can move in a particular situation.

BTW you will find are plenty of "real life" applications of eigenvalues and vectors.They turn up in most branches of physics and engineering, not to mention unexpected places like Google's "PageRank" algorithm for web searching!