Show that the given matrix is nilpotent, and then use this fact to find the matrix exponential eAt. A= −9 9 −1 −9 9 1 0 0 0
Show that the given matrix is nilpotent, and then use this fact to find the matrix exponential eAt. A= −9 9 −1 −9 9 1 0 0 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show that the given matrix is nilpotent, and then use this fact to find the matrix exponential
eAt.
A=
| −9 | 9 | −1 | ||
| −9 | 9 | 1 | ||
| 0 | 0 | 0 |
A nilpotent matrix is a matrix A such that
equals
for some positive integer n. The smallest such n for which this holds for the given matrix is
▼
Upper A Superscript nAn
left parenthesis AA Superscript Upper T Baseline right parenthesis Superscript nAATn
left parenthesis Upper A plus Upper I right parenthesis Superscript n(A+I)n
left parenthesis Upper A minus Upper I right parenthesis Superscript n(A−I)n
▼
the identity matrix
itself
its own transpose
the zero matrix
n=enter your response here,
for which the resulting matrix is
enter your response here.
(Use integers or fractions for any numbers in the expressions.)
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