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1 0 1 1 -1 1 *4. Let A = 1 1 -2 -1 1 1 5 a. Give the LU decomposition of A. b. Give the reduced echelon form of A.

1 0 1 1 -1 1 *4. Let A = 1 1 -2 -1 1 1 5 a. Give the LU decomposition of A. b. Give the reduced echelon form of A.

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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linear algebra 2.4 Q4

**Problem 4.** Let \( A = \begin{bmatrix} 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & -1 & 1 & 0 \\ 0 & 1 & -2 & -1 & 1 \\ 2 & 1 & 0 & 0 & 5 \end{bmatrix} \). a. Give the \( LU \) decomposition of \( A \). b. Give the reduced echelon form of \( A \).
Transcribed Image Text:**Problem 4.** Let \( A = \begin{bmatrix} 1 & 0 & 1 & 1 & 1 \\ 1 & 1 & -1 & 1 & 0 \\ 0 & 1 & -2 & -1 & 1 \\ 2 & 1 & 0 & 0 & 5 \end{bmatrix} \). a. Give the \( LU \) decomposition of \( A \). b. Give the reduced echelon form of \( A \).
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(a) The given matrix is not a square matrix, so we can use the Gauss elimination method with pivoting to 

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