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 |-

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 46E
icon
Related questions
Question
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage