I understand Gaussian elim and the inverse, but am new to Gaussian elim without pivot. Wordiness of the question is also throwing me off. Any help will be much appreciated, thanks in advance!
2026-03-24 23:41:47.1774395707
Gaussian Elimination without pivot
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Judging from how the question is worded, they seem to ask us not to use a permutation matrix, which in a literal sense means "pivoting" a matrix.
So solving with an A = LU Factorization should suffice. Which would involve working out E = I - A and then finding the inverse, as opposed to the more complete form PA = LU.
There wouldn't be a Gaussian Elimination without pivots, back substitution works on the fundamental idea of having pivots.
I hope that helps.
EDIT:
http://nptel.ac.in/courses/122104019/numerical-analysis/kadalbajoo/lec1/fnode5.html
Here is a small link depicting all three: