At the very least, your essay should cover the following questions:
What can happen that a matrix does not have an LU-factorization?
How and why does the multiplier method work?
How can LU-factorizations be used to solve linear systems?
The essay will be worth 50 points. Of these points, 20 are given for mathematical correctness, 10 points for
detailed and comprehensible explanations, 10 points for the structure/organization of your essay, and 10
points for the use of examples (make up your own examples) and illustrations.