(11) Let A = with ei genralues de,2g. Find aeo such that A3 + 12 - 0. (Hint : Cat6)3 = (a3+&3) + 3ab Cate))
(11) Let A = with ei genralues de,2g. Find aeo such that A3 + 12 - 0. (Hint : Cat6)3 = (a3+&3) + 3ab Cate))
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
![### Problem 11
Let
\[ A = \begin{bmatrix} a & 1 \\ 1 & 1 \end{bmatrix} \]
with eigenvalues \(\lambda_1, \lambda_2\). Find \(a \in \mathbb{C}\) such that \(\lambda_1^3 + \lambda_2^3 = 0\).
**Hint:** \((a+b)^3 = (a^3+b^3) + 3ab(a+b)\)
---
The following problems use:
a) \(\det(AB) = \det(A)\det(B)\)
b) \(\det(I) = 1\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ea29327-e72d-4002-ab87-7427c74c1ebe%2F9db0aa8c-ae98-4c3e-833e-92f27658593d%2Fhlea3qj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 11
Let
\[ A = \begin{bmatrix} a & 1 \\ 1 & 1 \end{bmatrix} \]
with eigenvalues \(\lambda_1, \lambda_2\). Find \(a \in \mathbb{C}\) such that \(\lambda_1^3 + \lambda_2^3 = 0\).
**Hint:** \((a+b)^3 = (a^3+b^3) + 3ab(a+b)\)
---
The following problems use:
a) \(\det(AB) = \det(A)\det(B)\)
b) \(\det(I) = 1\)
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