10) Let A E Mnxn be given by 0 0 ao ... -1 .. A = -1 0 a2 .. 0 0 0 • -1 an-1 .. Compute XA(t).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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10) Let A E Mnxn be given by
ao
...
-1
..
A =
-1 0
a2
...
0 0 0 ..
-1 An-1
Compute XA(t).
•..
Transcribed Image Text:10) Let A E Mnxn be given by ao ... -1 .. A = -1 0 a2 ... 0 0 0 .. -1 An-1 Compute XA(t). •..
11) Determine whether the matrix A is diagonalizable over R or C. If so, find
an invertible matrix Q and a diagonal matrix D such that A =
QDQ-. If not,
explain why.
[o 0
1
a) A = |1 0
0 1
А -
-1
1
3
1
b) A =
4
2
-1
-1 1
1
c) A = |1 1
1
1
1 1
d) A = |0 1 0
0 1 0
1
Transcribed Image Text:11) Determine whether the matrix A is diagonalizable over R or C. If so, find an invertible matrix Q and a diagonal matrix D such that A = QDQ-. If not, explain why. [o 0 1 a) A = |1 0 0 1 А - -1 1 3 1 b) A = 4 2 -1 -1 1 1 c) A = |1 1 1 1 1 1 d) A = |0 1 0 0 1 0 1
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