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Let A be the matrix given below, in which a and b are real numbers. 0 0 b A = 0 a a 0 0 0 a 0 0 0 0 b (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagona D such that A = PDP-¹).

Let A be the matrix given below, in which a and b are real numbers. 0 0 b A = 0 a a 0 0 0 a 0 0 0 0 b (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagona D such that A = PDP-¹).

Advanced Engineering Mathematics
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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show how A is diagonalizable for the values chosen and how it isn't diagonalizable for other values and explain both cases and why you picked the values you did, thanks

Let A be the matrix given below, in which a and b are real numbers. 1 00 b 0 a a 0 00 α 0 000 b A = (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A = PDP-¹).
Transcribed Image Text:Let A be the matrix given below, in which a and b are real numbers. 1 00 b 0 a a 0 00 α 0 000 b A = (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A = PDP-¹).
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