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  3. let a = 0 1 1 0 (a) calculate the matrix e

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

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Advance Math

Let A =

01
10

(a) Calculate the matrix exponential e^(At). (Hint: It mighthelp to write down the power series expansions for the hyperbolicfunctions
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 nonhomogeneousinitial value problem
x' =

01
10

x +

2
-1

, x(0) =

1
2

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

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