Please see attachment for full problem description and hint.
The solution of the vector-valued differential equation
dX/dt = AX(t) with X(0) = [a1
is given by:
X(t) = Exp(tA)X(0) = e^tA(X(0))
Explain how you would compute e^tA, and then find the general solution when:
A = [ 0 1 0
0 0 1
-1 1 1]
This solution calculates the characteristic of the matrix and finds all its eigenvalues.
Finding Eigenvalues / Eigenfunctions for Integral Operators
Please see the attached file for the fully formatted problems.
Find the eigenvalues and eigenfunctions for the integral operator
How would we solve the same problem if ?
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