1. Consider the matrix below for this item: A = -1 0 -1 1-5 -5 1.1. Set up A - AI and write down the characteristic polynomial p(x). 1.2. Solve for the eigenvalues of A. (For this item, you may use software or a website to calculate the roots of the characteristic polynomial; please just mention which software or website you used. You may also solve for the roots manually or by hand if you want.) 1.3. For each eigenvalue A₁, provide a corresponding eigenvector. Can we readily use the eigenvalues we solved for in item # 2 to determine the definiteness of A? Why or why not? (Limit your answer to just one sentence; use the premise or assumption of the theorem we studied under "Definiteness and Eigenvalues" in the slides.)
1. Consider the matrix below for this item: A = -1 0 -1 1-5 -5 1.1. Set up A - AI and write down the characteristic polynomial p(x). 1.2. Solve for the eigenvalues of A. (For this item, you may use software or a website to calculate the roots of the characteristic polynomial; please just mention which software or website you used. You may also solve for the roots manually or by hand if you want.) 1.3. For each eigenvalue A₁, provide a corresponding eigenvector. Can we readily use the eigenvalues we solved for in item # 2 to determine the definiteness of A? Why or why not? (Limit your answer to just one sentence; use the premise or assumption of the theorem we studied under "Definiteness and Eigenvalues" in the slides.)
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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Transcribed Image Text:1. Consider the matrix below for this item:
A =
-5 -5
1.1. Set up A - AI and write down the characteristic polynomial p(1).
1.2. Solve for the eigenvalues of A. (For this item, you may use software or a
website to calculate the roots of the characteristic polynomial; please just mention which
software or website you used. You may also solve for the roots manually or by hand if you
want.)
1.3. For each eigenvalue A₁, provide a corresponding eigenvector.
Can we readily use the eigenvalues we solved for in item # 2 to determine the
definiteness of A? Why or why not? (Limit your answer to just one sentence; use the premise
or assumption of the theorem we studied under "Definiteness and Eigenvalues" in the
slides.)
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