-) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show that A == B.
-) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show that A == B.
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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![(a) Let A, B be nx n symmetric matrices such that XTAX = XTBX for all
column vectors X e R". Show that A = B.
(b) Consider the quadratic form q = 2x3 +x3 – 4x1T2+4x2x3. Find a change
of variables that will diagonalize q. What is the resulting diagonalized
quadratic form?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75b475b2-d962-46fd-8ad5-09ef3eefcab4%2Fae52f94a-6fcb-448d-bc16-e58addc3fa6b%2Fo8p8a3_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let A, B be nx n symmetric matrices such that XTAX = XTBX for all
column vectors X e R". Show that A = B.
(b) Consider the quadratic form q = 2x3 +x3 – 4x1T2+4x2x3. Find a change
of variables that will diagonalize q. What is the resulting diagonalized
quadratic form?
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