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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff258f736-2efe-4abc-a546-b1bd73d984a7%2Fbd52a834-218a-4f02-b889-7364abf76bf6%2Fuq8xt2c_processed.png&w=3840&q=75)
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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