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- 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

1

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