Proof of LU-Factorization/Decomposition for Square Matrices

Reduce A to an upper Triangular Matrix U

Find the Elementary Matrix Related to Column 1

Find the Elementary Matrix Related to Column 2

Find the Elementary Matrix Related to Column 3

Find the Elementary Matrix Related to Column 4

Find the Elementary Matrix Related to Column 5

Find the Elementary Matrix Related to Column 5n-1

Find the Lower Triangular Matrix L

LU-Factorization/Decomposition Using Elementary Matrices

LU-Factorization/Decomposition Using The Multiplier Method

LU-Factorization Using a Direct Method

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