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Find the LU 2 a) A = b) B= 1 Factorization of the given matrix 2 2 4 - 2 1 -4 1 2 12 1 3

Find the LU 2 a) A = b) B= 1 Factorization of the given matrix 2 2 4 - 2 1 -4 1 2 12 1 3

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 11E: 11. Find two nonzero matrices and such that.
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Advanced Math - LU Factorization

Solve the given equations by LU-Factorization. Example is in the second pic. 

Find the LU Factorization of the given matrix a) A = b) B = 2-2 1 2 4 2 1 -4 1 2 12 1 3
Transcribed Image Text:Find the LU Factorization of the given matrix a) A = b) B = 2-2 1 2 4 2 1 -4 1 2 12 1 3
Example Find the LU-factorization of -1 2-4 A = 2-5 10 3 1 6 Solution A = Step 1: I Step 1: -1 2 - 4 2-5 10 3 1 6 2R₁ + R₂ 3R₁ + R3 10 010 0 0 1 record 2 record - 3 -1 2-4 A: 2 - 5 10 -1 2 0 - 1 0 7 3 1 6 4 2 - 6 Step 2: 7R2 + R3 1 0 0 -2 1 0 Step 2: record -7 -3 0 1, L 0 0 -1 From the elementary row operations, we get the LU-Factorization of A. -1 2 -GD-GA -2 1 0 -3 7 1 -1 2-4 0 - 1 2 0 08 2 1 100 -2 1 0 -3 7 1, 0 - U 4 2 8
Transcribed Image Text:Example Find the LU-factorization of -1 2-4 A = 2-5 10 3 1 6 Solution A = Step 1: I Step 1: -1 2 - 4 2-5 10 3 1 6 2R₁ + R₂ 3R₁ + R3 10 010 0 0 1 record 2 record - 3 -1 2-4 A: 2 - 5 10 -1 2 0 - 1 0 7 3 1 6 4 2 - 6 Step 2: 7R2 + R3 1 0 0 -2 1 0 Step 2: record -7 -3 0 1, L 0 0 -1 From the elementary row operations, we get the LU-Factorization of A. -1 2 -GD-GA -2 1 0 -3 7 1 -1 2-4 0 - 1 2 0 08 2 1 100 -2 1 0 -3 7 1, 0 - U 4 2 8
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