(1) 2 (c) Let A = -1 0 Find an orthogonal matrix P such that PT AP = D where D is a diagonal matrix D. [Show your calculation clearly and check your answer.]
(1) 2 (c) Let A = -1 0 Find an orthogonal matrix P such that PT AP = D where D is a diagonal matrix D. [Show your calculation clearly and check your answer.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer c
![(a) State the axioms that the inner product (, ) satisfies.
(b) Let P2 be the vector space of real polynomials of degree < 2. Suppose
P2 is endowed with the inner product (p, q) = So P(x)q(x) dx.
i. Use the Gram-Schmidt process to convert B = {x+1, x – 1, x?} into
%3D
an orthogonal basis.
ii. Find, with explanation, a basis for U- if U = {ax + b: a,b € R}.
2
(c) Let A =
1
-1 0
1
Find an orthogonal matrix P such that PT AP = D where D is a diagonal
matrix D.
(Show your calculation clearly and check your answer.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03d2c951-aaca-436c-8d97-0e13a64c0979%2F721f97e9-fc24-4fc5-869f-a4b30559cd81%2Fe7dgfbe_processed.png&w=3840&q=75)
Transcribed Image Text:(a) State the axioms that the inner product (, ) satisfies.
(b) Let P2 be the vector space of real polynomials of degree < 2. Suppose
P2 is endowed with the inner product (p, q) = So P(x)q(x) dx.
i. Use the Gram-Schmidt process to convert B = {x+1, x – 1, x?} into
%3D
an orthogonal basis.
ii. Find, with explanation, a basis for U- if U = {ax + b: a,b € R}.
2
(c) Let A =
1
-1 0
1
Find an orthogonal matrix P such that PT AP = D where D is a diagonal
matrix D.
(Show your calculation clearly and check your answer.]
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