Section 2.5 -4 27 --- -4 5 2 and b = 0. Given that A has an LU factorization 6 -9 1. Let A = 2 1 0 -2 1 0 0 -1 1 دن use this LU factorization to solve Ax = b. 2 -4 2 0-3 6 0 0 1
Section 2.5 -4 27 --- -4 5 2 and b = 0. Given that A has an LU factorization 6 -9 1. Let A = 2 1 0 -2 1 0 0 -1 1 دن use this LU factorization to solve Ax = b. 2 -4 2 0-3 6 0 0 1
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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Question
![**Section 2.5**
1. Let \( A = \begin{bmatrix} 2 & -4 & 2 \\ -4 & 5 & 2 \\ 6 & -9 & 1 \end{bmatrix} \) and \( \mathbf{b} = \begin{bmatrix} 6 \\ 0 \\ 6 \end{bmatrix} \). Given that \( A \) has an \( LU \) factorization
\[
\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 3 & -1 & 1 \end{bmatrix}
\begin{bmatrix} 2 & -4 & 2 \\ 0 & -3 & 6 \\ 0 & 0 & 1 \end{bmatrix},
\]
use this \( LU \) factorization to solve \( A\mathbf{x} = \mathbf{b} \).
2. Find the \( LU \) factorizations of
\[
\begin{bmatrix} 2 & 0 & 5 & 2 \\ -6 & 3 & -13 & -3 \\ 4 & 9 & 16 & 17 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 & 3 & 2 \\ 4 & 13 & 9 \\ -6 & 5 & 4 \end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F327c4acc-aab0-4600-9811-c42079067cf3%2F9d268b11-4267-43c7-bbfc-22c4fbf7ab3f%2F575b88k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Section 2.5**
1. Let \( A = \begin{bmatrix} 2 & -4 & 2 \\ -4 & 5 & 2 \\ 6 & -9 & 1 \end{bmatrix} \) and \( \mathbf{b} = \begin{bmatrix} 6 \\ 0 \\ 6 \end{bmatrix} \). Given that \( A \) has an \( LU \) factorization
\[
\begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 3 & -1 & 1 \end{bmatrix}
\begin{bmatrix} 2 & -4 & 2 \\ 0 & -3 & 6 \\ 0 & 0 & 1 \end{bmatrix},
\]
use this \( LU \) factorization to solve \( A\mathbf{x} = \mathbf{b} \).
2. Find the \( LU \) factorizations of
\[
\begin{bmatrix} 2 & 0 & 5 & 2 \\ -6 & 3 & -13 & -3 \\ 4 & 9 & 16 & 17 \end{bmatrix}
\]
and
\[
\begin{bmatrix} 2 & 3 & 2 \\ 4 & 13 & 9 \\ -6 & 5 & 4 \end{bmatrix}
\]
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