-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

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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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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