50. Let A = a c 2 d] (a) Prove that A is diagonalizable if (ad)² + 4bc> 0 and is not diagonalizable if (a - d)² - 4bc < 0. (b) Find two examples to demonstrate that if (ad)² + 4bc = 0, then A may or may not be diagonalizable.
50. Let A = a c 2 d] (a) Prove that A is diagonalizable if (ad)² + 4bc> 0 and is not diagonalizable if (a - d)² - 4bc < 0. (b) Find two examples to demonstrate that if (ad)² + 4bc = 0, then A may or may not be diagonalizable.
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
Please show all work when solving this proof
![= [a b]
c d
50. Let A =
(a) Prove that A is diagonalizable if (a - d)² +
4bc> 0 and is not diagonalizable if (a − d)² +
4bc < 0.
(b) Find two examples to demonstrate that if
(a - d)² + 4bc = 0, then A may or may not be
diagonalizable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb82eee3-c597-43b7-b98f-cffc18fbca72%2F6e9e0dc1-855d-44ed-ad59-2885145aab7a%2Ftdmnw3_processed.png&w=3840&q=75)
Transcribed Image Text:= [a b]
c d
50. Let A =
(a) Prove that A is diagonalizable if (a - d)² +
4bc> 0 and is not diagonalizable if (a − d)² +
4bc < 0.
(b) Find two examples to demonstrate that if
(a - d)² + 4bc = 0, then A may or may not be
diagonalizable.
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