uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is positive definite when c> he quadratic form is positive semi-definite when c> he quadratic form Qis indefinite when |c| < he quadratic form is negative semi-definite when c < he quadratic form Q is negative semi-definite when c< II N c) and x = X2
uppose is the quadratic form Q = x Ax, where A is the symmetric matrix A = 2 he quadratic form is positive definite when c> he quadratic form is positive semi-definite when c> he quadratic form Qis indefinite when |c| < he quadratic form is negative semi-definite when c < he quadratic form Q is negative semi-definite when c< II N c) and x = X2
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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Question
![Suppose is the quadratic form Q = x¹ Ax, where A is the symmetric matrix A =
The quadratic form is positive definite when c >
The quadratic form is positive semi-definite when c
The quadratic form is indefinite when |c| <
The quadratic form is negative semi-definite when c <
- (22) and
The quadratic form Qis negative semi-definite when c<
and x =
(21).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b609ed5-0879-4e23-8eee-4515e84ef2b9%2F66f4f621-25c6-4752-8009-5f8df40e6d87%2Fdvt8cd_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose is the quadratic form Q = x¹ Ax, where A is the symmetric matrix A =
The quadratic form is positive definite when c >
The quadratic form is positive semi-definite when c
The quadratic form is indefinite when |c| <
The quadratic form is negative semi-definite when c <
- (22) and
The quadratic form Qis negative semi-definite when c<
and x =
(21).
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