Finding LU-Factorization/Decomposition Using Elementary Matrices

Before we begin LU-Factorization using Elementary Matrices, let us get a good understanding of Elementary Matrices and how they work.

Practice: Determine Whether or Not the Give Matrix is Elementary

Using Elementary Matrices and a Given Matrix to Write Another Matrix

Practice: Write the matrix A in row-echelon form and let this matrix be called B. Then write the matrix B using a sequence of elementary matrices.

LU-Factorization of a Square Matrix

Note:

Finding an LU-Factorization of a Square Matrix Using Elementary Matrices

Proof of LU-Factorization/Decomposition for Square Matrices

Practice 1: Find the LU-Factorization of the given matrix using Elementary Matrices.

Practice 2:

LU-Factorization/Decomposition Using The Multiplier Method

LU-Factorization Using a Direct Method

Also, you can find the LU-Factorization of a non-square matrix (post coming soon).

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