-14 2 4 Let A= 2 -17 2 Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D=PTAP. 4 2 -14 D= Note: You'll probably need to do a little bit of extra work to ensure that each entry in P is a rational number

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 5SE: Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why...
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Question
-14
2
4
Let A =
2
-17
2
Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D = PT AP
4
2
-14
D=
Note: You'll probably need to do a little bit of extra work to ensure that each entry in P is a rational number
Transcribed Image Text:-14 2 4 Let A = 2 -17 2 Find an orthogonal matrix P with rational entries and a diagonal matrix D such that D = PT AP 4 2 -14 D= Note: You'll probably need to do a little bit of extra work to ensure that each entry in P is a rational number
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