Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

For 1.3.3, you don't need to solve it just find the determinant for 1.3.9

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:1.3.3 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).
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?
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?
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Determinant
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS