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Problem 1. Consider a system of linear equations Ax = b where 2 3] 1 6, x = A = 4 6 -2 2 X1 -B X2 X3 22 b = 42 28 a. Perform an LU decomposition for A. b. Using your LU decomposition solve the system of equations for x.

Problem 1. Consider a system of linear equations Ax = b where 2 3] 1 6, x = A = 4 6 -2 2 X1 -B X2 X3 22 b = 42 28 a. Perform an LU decomposition for A. b. Using your LU decomposition solve the system of equations for x.

Advanced Engineering Mathematics
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 1.** Consider a system of linear equations \( Ax = b \) where \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 1 & 6 \\ 6 & -2 & 2 \end{bmatrix}, \quad x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}, \quad b = \begin{bmatrix} 22 \\ 42 \\ 28 \end{bmatrix}. \] a. Perform an LU decomposition for \( A \). b. Using your LU decomposition solve the system of equations for \( x \).
Transcribed Image Text:**Problem 1.** Consider a system of linear equations \( Ax = b \) where \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 1 & 6 \\ 6 & -2 & 2 \end{bmatrix}, \quad x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}, \quad b = \begin{bmatrix} 22 \\ 42 \\ 28 \end{bmatrix}. \] a. Perform an LU decomposition for \( A \). b. Using your LU decomposition solve the system of equations for \( x \).
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