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[1 a b Let A = 0 5 2 0 0 1 (а) (i) Determine the condition of a and b so that A is diagonalisable. (ii) Let a = 2 and b 0. Find the Jordan canonical form for A. (b) Let f(t) = (t- 2)*(t +1)² be the characteristic polynomial for a linear operator T. Obtain all Jordan canonical forms for T.

[1 a b Let A = 0 5 2 0 0 1 (а) (i) Determine the condition of a and b so that A is diagonalisable. (ii) Let a = 2 and b 0. Find the Jordan canonical form for A. (b) Let f(t) = (t- 2)*(t +1)² be the characteristic polynomial for a linear operator T. Obtain all Jordan canonical forms for T.

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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[1 Let A = |0 5 2 0 0 1 a b (а) (i) Determine the condition of a and b so that A is diagonalisable. Let a = 2 and b=0. Find the Jordan canonical form for A. (ii) (b) Let f(t) = (t – 2)*(t + 1)² be the characteristic polynomial for a linear operator T. Obtain all Jordan canonical forms for T.
Transcribed Image Text:[1 Let A = |0 5 2 0 0 1 a b (а) (i) Determine the condition of a and b so that A is diagonalisable. Let a = 2 and b=0. Find the Jordan canonical form for A. (ii) (b) Let f(t) = (t – 2)*(t + 1)² be the characteristic polynomial for a linear operator T. Obtain all Jordan canonical forms for T.
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