Find permutation matrix P, unit lower triangular matrix L, and upper triangular matrix U such that A = PLU.
Added by James W.
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First, we need to find the LU decomposition of matrix A. This can be done using Gaussian elimination or any other suitable method. Let's assume that we have found the following LU decomposition: A = LU where L is a unit lower triangular matrix and U is an upper Show more…
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Consider the matrix. Applying elementary row operations to reduce this matrix to upper triangular form can be written as: Hence, or otherwise, write down decomposition of the form PA = LU; where P is a permutation matrix (or the identity matrix if no permutation is needed), L is lower triangular, and U is upper triangular.
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