Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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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**Problem Statement:**

Find an LU factorization for the matrix \( A = \begin{pmatrix} -2 & 3 & 0 \\ 4 & 1 & 2 \\ -3 & 3 & -2 \end{pmatrix} \). Verify that \( LU = A \).

**Explanation:**

In this problem, you are tasked with performing an LU factorization on the given 3x3 matrix. LU factorization involves decomposing the matrix \( A \) into two matrices: \( L \), a lower triangular matrix, and \( U \), an upper triangular matrix such that \( A = LU \).

Once the factorization is done, you will need to verify your result by multiplying \( L \) and \( U \) to ensure that their product gives back the original matrix \( A \). This is a crucial step to confirm the accuracy of your LU factorization.
Transcribed Image Text:**Problem Statement:** Find an LU factorization for the matrix \( A = \begin{pmatrix} -2 & 3 & 0 \\ 4 & 1 & 2 \\ -3 & 3 & -2 \end{pmatrix} \). Verify that \( LU = A \). **Explanation:** In this problem, you are tasked with performing an LU factorization on the given 3x3 matrix. LU factorization involves decomposing the matrix \( A \) into two matrices: \( L \), a lower triangular matrix, and \( U \), an upper triangular matrix such that \( A = LU \). Once the factorization is done, you will need to verify your result by multiplying \( L \) and \( U \) to ensure that their product gives back the original matrix \( A \). This is a crucial step to confirm the accuracy of your LU factorization.
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