3. Let A be a real number, and let J = (a) Compute J2, J³, and J4. (b) Use an inductive argument to show r-() Jn = %3D (c) Based on the result in part (b), show that et tet exp(Jt) = ( 0. ete

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. Let A be a real number, and let
J =
(a) Compute J², J3, and J4.
(b) Use an inductive argument to show
Jn =
(c) Based on the result in part (b), show that
exp(Jt) = (
elt
tert
0 ett
(d) Based on the result in part (c) and that exp(Jt) is the special fundamental matrix
(t), solve the initial value problem
with 7(0) = 7
%3D
Transcribed Image Text:3. Let A be a real number, and let J = (a) Compute J², J3, and J4. (b) Use an inductive argument to show Jn = (c) Based on the result in part (b), show that exp(Jt) = ( elt tert 0 ett (d) Based on the result in part (c) and that exp(Jt) is the special fundamental matrix (t), solve the initial value problem with 7(0) = 7 %3D
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