The matrix S is not positive definite. Find a vector x such that x" Sx < 0. 5 6 S = 6 7
The matrix S is not positive definite. Find a vector x such that x" Sx < 0. 5 6 S = 6 7
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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![The matrix \( S \) is not positive definite. Find a vector \( \mathbf{x} \) such that \( \mathbf{x}^T S \mathbf{x} < 0 \).
\[
S = \begin{bmatrix} 5 & 6 \\ 6 & 7 \end{bmatrix}
\]
In this problem, you're asked to find a vector \( \mathbf{x} \) such that the quadratic form \( \mathbf{x}^T S \mathbf{x} \) is negative. The matrix \( S \) is a 2x2 symmetric matrix, and you're given that it is not positive definite.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7297a90f-0927-4369-b782-4368eb3beb88%2F7018cdd9-8f4b-473d-89a8-fcff360fc3da%2Fe4hm8tv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The matrix \( S \) is not positive definite. Find a vector \( \mathbf{x} \) such that \( \mathbf{x}^T S \mathbf{x} < 0 \).
\[
S = \begin{bmatrix} 5 & 6 \\ 6 & 7 \end{bmatrix}
\]
In this problem, you're asked to find a vector \( \mathbf{x} \) such that the quadratic form \( \mathbf{x}^T S \mathbf{x} \) is negative. The matrix \( S \) is a 2x2 symmetric matrix, and you're given that it is not positive definite.
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