Show that the matrix A = et. Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem. Substitute the value of r and the smallest value of k that solve the equation. 0 0 -1 -3 -3 1 0 1 At 0 1 0 00 1 satisfies (A - rI)* = 0 for some number r and some positive integer k and use this fact to determine the matrix -1 -3 -3 What is eat? 100 -1) 0 1 0 001 3 C... = 0
Show that the matrix A = et. Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem. Substitute the value of r and the smallest value of k that solve the equation. 0 0 -1 -3 -3 1 0 1 At 0 1 0 00 1 satisfies (A - rI)* = 0 for some number r and some positive integer k and use this fact to determine the matrix -1 -3 -3 What is eat? 100 -1) 0 1 0 001 3 C... = 0
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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Subject: algebra
Transcribed Image Text:Show that the matrix A =
eAt. Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem.
0 1 0
0 0 1 satisfies (A - rI)* = 0 for some number r and some positive integer k and use this fact to determine the matrix
-1 -3 -3
Substitute the value of r and the smallest value of k that solve the equation.
0
1 0
0 0
1
-1 -3 -3
What is eat?
At
100
-1) 0 1 0
001
3
= 0
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