1.3.3 Find the triangular factors L and U of 1 1 0 0 1 1 A = 1 2 1 0 0 1 2 In this case U is the same as L'. What is the pivot matrix D? Solve Lc=b and Ux=c if b= (1, 0, 0, O).
1.3.3 Find the triangular factors L and U of 1 1 0 0 1 1 A = 1 2 1 0 0 1 2 In this case U is the same as L'. What is the pivot matrix D? Solve Lc=b and Ux=c if b= (1, 0, 0, O).
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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For 1.3.3, you don't need to solve it just find the determinant for 1.3.9
Transcribed Image Text:1.3.3 Find the triangular factors L and U of
1
1 0 0
1
A =
2 1 0
1
2
01 2
In this case U is the same as L'. What is the pivot matrix D? Solve Lc =b and Ux = c if
b = (1, 0, 0, 0).
Transcribed Image Text:1.3.9 (i) The determinant of a triangular matrix is the product of the entries on the
agonal. Thus det L= 1 and
det A
det LDL" = (det L)(det D)(det L")= det D.
The determinant is the product of the pivots. Show that det A>0 if A is positive definite.
(ii) Give an example with det A>0 in which A is not positive definite.
tiii) What is the determinant of A in Exercise 1.3.3?
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