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
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0da8f1c9-4343-4f72-a6f1-5d707869b084%2F81e3bd0e-c1c0-4fda-82e5-2f9ccb31d777%2Fn8yq6pw_processed.png&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0da8f1c9-4343-4f72-a6f1-5d707869b084%2F81e3bd0e-c1c0-4fda-82e5-2f9ccb31d777%2Fiqs5xon_processed.png&w=3840&q=75)
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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