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Let 31 A 1 0 2 120 a) Note the Eigenvalues are 1,4,and -2. Find the normalized Eigenvectors of A and use them to construct an orthogonal Matrix Q. Verify that Q is orthognal. Verify that A = QDQ where D = diag(1, 4, -2). b) Show that QTAQ = D.

Let 31 A 1 0 2 120 a) Note the Eigenvalues are 1,4,and -2. Find the normalized Eigenvectors of A and use them to construct an orthogonal Matrix Q. Verify that Q is orthognal. Verify that A = QDQ where D = diag(1, 4, -2). b) Show that QTAQ = D.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Let A = 31 102 120 a) Note the Eigenvalues are 1,4,and -2. Find the normalized Eigenvectors of A and use them to construct an orthogonal Matrix Q. Verify that Q is orthognal. Verify that A = QDQT where D = = diag(1,4, -2). b) Show that QTAQ = D.
Transcribed Image Text:1. Let A = 31 102 120 a) Note the Eigenvalues are 1,4,and -2. Find the normalized Eigenvectors of A and use them to construct an orthogonal Matrix Q. Verify that Q is orthognal. Verify that A = QDQT where D = = diag(1,4, -2). b) Show that QTAQ = D.
4. Return to Question 1. Assuming that {e} is IID and normally distributed, com- pute a 99% confidence interval for the trend slope parameter a and the intercept parameter u. Does it bother you that the interval for u contains negative numbers? Discuss.
Transcribed Image Text:4. Return to Question 1. Assuming that {e} is IID and normally distributed, com- pute a 99% confidence interval for the trend slope parameter a and the intercept parameter u. Does it bother you that the interval for u contains negative numbers? Discuss.
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