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For each of the following matrices A E M,(R), test A for diagonalisabil- ity. If A is diagonalisable, find an invertible matrix Q and a diagonal matrix D such that D = Q-'AQ. [Take care: the field is R, not C.] 1 2 (a) 0 1 (: :) 1 3 (b) 3 1 -4 0` (c) |8 -5 0 6 -6 3 1 (d) 1 0 -1 0 1 1 (1 1 0 (e) 0 1 2 0 0 3

For each of the following matrices A E M,(R), test A for diagonalisabil- ity. If A is diagonalisable, find an invertible matrix Q and a diagonal matrix D such that D = Q-'AQ. [Take care: the field is R, not C.] 1 2 (a) 0 1 (: :) 1 3 (b) 3 1 -4 0` (c) |8 -5 0 6 -6 3 1 (d) 1 0 -1 0 1 1 (1 1 0 (e) 0 1 2 0 0 3

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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Linear Transformations. Parts c), d) and e) please

For each of the following matrices A E M,(R), test A for diagonalisabil- ity. If A is diagonalisable, find an invertible matrix Q and a diagonal matrix D such that D = Q-'AQ. [Take care: the field is R, not C.] 1 2 (a) 0 1 (: :) 1 3 (b) 3 1 -4 0` (c) |8 -5 0 6 -6 3 1 (d) 1 0 -1 0 1 1 (1 1 0 (e) 0 1 2 0 0 3
Transcribed Image Text:For each of the following matrices A E M,(R), test A for diagonalisabil- ity. If A is diagonalisable, find an invertible matrix Q and a diagonal matrix D such that D = Q-'AQ. [Take care: the field is R, not C.] 1 2 (a) 0 1 (: :) 1 3 (b) 3 1 -4 0` (c) |8 -5 0 6 -6 3 1 (d) 1 0 -1 0 1 1 (1 1 0 (e) 0 1 2 0 0 3
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