A matrix A has a LU factorization if A = LU where L is a lower triangular matrix (a matrix with zeros above diagonal) and U is an upper triangular matrix (a matrix with zeros below the diagonal). 4 3 (a) Verify that A = -4 -5 7 Is a product of a L=-1 -G 8 6 -8 100] [4 3 -5 10 and U = 0 -2 2 201 0 0 2 (b) Use the LU factorization to solve Az = H -4 for . To do so, first solve Ly = 6, and after Uz = y. (c) Find L-¹ and U-¹, then use these to find A-¹ showing that A is invertible.
A matrix A has a LU factorization if A = LU where L is a lower triangular matrix (a matrix with zeros above diagonal) and U is an upper triangular matrix (a matrix with zeros below the diagonal). 4 3 (a) Verify that A = -4 -5 7 Is a product of a L=-1 -G 8 6 -8 100] [4 3 -5 10 and U = 0 -2 2 201 0 0 2 (b) Use the LU factorization to solve Az = H -4 for . To do so, first solve Ly = 6, and after Uz = y. (c) Find L-¹ and U-¹, then use these to find A-¹ showing that A is invertible.
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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