CSCI 5606, Assignment 3

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Problem 1. Prove that if a nonsingular matrix A has an LU factorization in which L is a
unit lower triangular matrix, then L and U are unique.
Problem 2. Find the LU factorization of the following matrix
A =



3 0 1
0 −1 3
1 3 0



in which L is lower triangular and U is unit upper triangular.
Problem 3. For
A =

1 5
3 17 #
find all LU factorizations and all UL factorizations in which L is unit lower triangular.
Problem 4. Write a Cholesky factorization program and test it by solving the following
problem



0.05×1 + 0.07×2 + 0.06×3 + 0.05×4 = 0.23
0.07×1 + 0.10×2 + 0.08×3 + 0.07×4 = 0.32
0.06×1 + 0.08×2 + 0.10×3 + 0.09×4 = 0.33
0.05×1 + 0.07×2 + 0.09×3 + 0.10×4 = 0.31
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