Find the LU factorization of A = -4 5-5 8-614 That is, write A = LU where L is a lower triang with ones on the diagonal, and I is an upper tr matrix
Find the LU factorization of A = -4 5-5 8-614 That is, write A = LU where L is a lower triang with ones on the diagonal, and I is an upper tr matrix
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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![**LU Factorization Problem**
**Objective:** Find the LU factorization of matrix \( A \).
\[ A = \begin{bmatrix} -4 & 5 & -5 \\ 8 & -6 & 14 \end{bmatrix} \]
**Instructions:** Write \( A = LU \), where \( L \) is a lower triangular matrix with ones on the diagonal, and \( U \) is an upper triangular matrix.
The task is to express matrix \( A \) as the product of matrices \( L \) and \( U \).
\[ A = \begin{bmatrix} \hspace{1em} & \hspace{1em} & \hspace{1em} \\ \hspace{1em} & \hspace{1em} & \hspace{1em} \end{bmatrix} \begin{bmatrix} \hspace{1em} & \hspace{1em} & \hspace{1em} \\ \hspace{1em} & \hspace{1em} & \hspace{1em} \end{bmatrix} \]
**Note:** Fill in the matrices above to complete the LU factorization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d4f07e6-ff0e-4dd7-9b82-622a270b91d8%2F27ecc1b8-83f6-4d61-a789-521f86e3ca3b%2Fr80se5r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**LU Factorization Problem**
**Objective:** Find the LU factorization of matrix \( A \).
\[ A = \begin{bmatrix} -4 & 5 & -5 \\ 8 & -6 & 14 \end{bmatrix} \]
**Instructions:** Write \( A = LU \), where \( L \) is a lower triangular matrix with ones on the diagonal, and \( U \) is an upper triangular matrix.
The task is to express matrix \( A \) as the product of matrices \( L \) and \( U \).
\[ A = \begin{bmatrix} \hspace{1em} & \hspace{1em} & \hspace{1em} \\ \hspace{1em} & \hspace{1em} & \hspace{1em} \end{bmatrix} \begin{bmatrix} \hspace{1em} & \hspace{1em} & \hspace{1em} \\ \hspace{1em} & \hspace{1em} & \hspace{1em} \end{bmatrix} \]
**Note:** Fill in the matrices above to complete the LU factorization.
Expert Solution
Step 1
Introduction:
Finding the inverse of a matrix and determining the determinant of a matrix are two applications of this method of factorising a matrix as the product of two triangular matrices. Solving a system of equations is another application, as is determining the current in a circuit and solving problems involving discrete dynamical systems.
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