**Problem Statement:**Find all \(\alpha\) such that the matrix \( \mathbf{A} \) is positive definite.\[\mathbf{A} = \begin{bmatrix}\alpha & 1 & -1 \\1 & 2 & 1 \\-1 & 1 & 4\end{bmatrix}\]

Answered: Image /qna-images/answer/0eddd393-8105-46b0-917a-662582071aac.jpg

Answered: Find all a so that A = α 1 -1 1 2 1 -1…

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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Find all a so that A = α 1 -1 1 2 1 -1 1 is positive definite. 4