Let A = 1 1 -2 2 1 -2 3 4 -2 i) Compute the LDV factorization of A, namely find the lower unitriangular matrix L, the diagonal matrix D, and the upper unitriangular matrix V such that A = LDV. ii) Find the LU factorization of AT using the matrices L, D, V obtained in i). iii) Use the matrices L, D, V obtained in i) to compute the determinant of A and AT.
Let A = 1 1 -2 2 1 -2 3 4 -2 i) Compute the LDV factorization of A, namely find the lower unitriangular matrix L, the diagonal matrix D, and the upper unitriangular matrix V such that A = LDV. ii) Find the LU factorization of AT using the matrices L, D, V obtained in i). iii) Use the matrices L, D, V obtained in i) to compute the determinant of A and AT.
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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Transcribed Image Text:Let
A =
1
1
-2
1
3
4 -2
2
-2
i) Compute the LDV factorization of A, namely find the lower unitriangular matrix L,
the diagonal matrix D, and the upper unitriangular matrix V such that A = LDV.
ii) Find the LU factorization of AT using the matrices L, D, V obtained in i).
iii) Use the matrices L, D, V obtained in i) to compute the determinant of A and AT.
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