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4. Assume that a matrix A satisfies P A = LU, where 10 0 (19). 3 4 P=100 010 2 L = 231 10, and U = 012 002 Use these factors, without forming the matrix A or taking any inverses, to solve the system of equations Ax = b, where b = (2, 10, −12)T. Show forward and back substitution by hand.

4. Assume that a matrix A satisfies P A = LU, where 10 0 (19). 3 4 P=100 010 2 L = 231 10, and U = 012 002 Use these factors, without forming the matrix A or taking any inverses, to solve the system of equations Ax = b, where b = (2, 10, −12)T. Show forward and back substitution by hand.

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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4. Assume that a matrix A satisfies PA = LU, where 001 1 0 0 100 (19) 010 - P = L = and U = 231 012 002 Use these factors, without forming the matrix A or taking any inverses, to solve the system of equations Ax = b, where b = (2, 10, -12)T. Show forward and back substitution by hand.
Transcribed Image Text:4. Assume that a matrix A satisfies PA = LU, where 001 1 0 0 100 (19) 010 - P = L = and U = 231 012 002 Use these factors, without forming the matrix A or taking any inverses, to solve the system of equations Ax = b, where b = (2, 10, -12)T. Show forward and back substitution by hand.
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