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For the linear system A=b as below 2 -1 0 -1 4 2 23. 0117 2 x₂ = diagonal, and U is a upper triangular. (c) Is A positive definite? Why? (a) Use Gaussian elimination to solve the following linear system. (b) Find the LU-factorization of A such that A = LU, where L is lower triar |-

For the linear system A=b as below 2 -1 0 -1 4 2 23. 0117 2 x₂ = diagonal, and U is a upper triangular. (c) Is A positive definite? Why? (a) Use Gaussian elimination to solve the following linear system. (b) Find the LU-factorization of A such that A = LU, where L is lower triar |-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the linear system A=b as below 2 -1 0 -1 4 2 0117 2 x₂ = [X3. |- 2 (a) Use Gaussian elimination to solve the following linear system. (b) Find the LU-factorization of A such that A = LU, where L is lower triangular with 1s on its diagonal, and U is a upper triangular. (c) Is A positive definite? Why? (d) Can you determine whether A has a Cholesky LLT factorization (A = LL^T) without actually computing for L? Why? Where L is a lower triangular matrix with positive diagonal values. (e) If your answer to part (d) is "yes", find such L.
Transcribed Image Text:For the linear system A=b as below 2 -1 0 -1 4 2 0117 2 x₂ = [X3. |- 2 (a) Use Gaussian elimination to solve the following linear system. (b) Find the LU-factorization of A such that A = LU, where L is lower triangular with 1s on its diagonal, and U is a upper triangular. (c) Is A positive definite? Why? (d) Can you determine whether A has a Cholesky LLT factorization (A = LL^T) without actually computing for L? Why? Where L is a lower triangular matrix with positive diagonal values. (e) If your answer to part (d) is "yes", find such L.
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