Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower triangular matrix with ones on the diagonal, D is a diagonal matrix, and U is an upper triangular matrix with ones on the diagonal. L = D = U =
Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower triangular matrix with ones on the diagonal, D is a diagonal matrix, and U is an upper triangular matrix with ones on the diagonal. L = D = U =
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
![**Find the LDU Factorization**
We are given the matrix:
\[
A = \begin{bmatrix}
-3 & -6 & 6 \\
-15 & -29 & 33 \\
-9 & -15 & 22
\end{bmatrix}
\]
Our goal is to factorize it as \(A = LDU\) where:
- \(L\) is a lower triangular matrix with ones on the diagonal.
- \(D\) is a diagonal matrix.
- \(U\) is an upper triangular matrix with ones on the diagonal.
### Matrices to find:
\[
L = \begin{bmatrix}
1 & & \\
& 1 & \\
& & 1
\end{bmatrix}
\]
\[
D = \begin{bmatrix}
& & \\
& & \\
& &
\end{bmatrix}
\]
\[
U = \begin{bmatrix}
1 & & \\
& 1 & \\
& & 1
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2192a9f0-1ae9-4ed3-a35b-fc11f1172fc0%2Faa0d44ad-afd9-4a1d-b76a-ee2855f1c630%2Focunhn6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the LDU Factorization**
We are given the matrix:
\[
A = \begin{bmatrix}
-3 & -6 & 6 \\
-15 & -29 & 33 \\
-9 & -15 & 22
\end{bmatrix}
\]
Our goal is to factorize it as \(A = LDU\) where:
- \(L\) is a lower triangular matrix with ones on the diagonal.
- \(D\) is a diagonal matrix.
- \(U\) is an upper triangular matrix with ones on the diagonal.
### Matrices to find:
\[
L = \begin{bmatrix}
1 & & \\
& 1 & \\
& & 1
\end{bmatrix}
\]
\[
D = \begin{bmatrix}
& & \\
& & \\
& &
\end{bmatrix}
\]
\[
U = \begin{bmatrix}
1 & & \\
& 1 & \\
& & 1
\end{bmatrix}
\]
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