Let A = 0 1 1 0 (a) Calculate the matrix exponential e^(At). (Hint: It might...

Let A =

0	1
1	0

(a) Calculate the matrix exponential e^(At). (Hint: It might help to write down the power series expansions for the hyperbolic functions
cosh(t) =(e^t + e^(−t))/2
and sinh(t) =(e^t −e^(−t))/2
and then try to write eAt in terms of these two functions.)
(b) Use your matrix from part (a) to solve the nonhomogeneous initial value problem
x' =

0	1
1	0

x +

-1

, x(0) =

. (Hint: You might need the identity cosh^2(t)−sinh^2(t) = 1.)

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Expert Solution

Colby Messinger answered 1 year ago

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