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## Homework Statement

Given x' = Ax where A =

( 0 1 )

( -1 0 )

Compute the matrix exponential and then find the solution such that x(0) =

( 1 )

( 2 )

## Homework Equations

## The Attempt at a Solution

I computed the matrix exponential and obtained the matrix,

e^(A) =

( cos(t) sin(t) )

( -sin(t) cos(t) )

But I don't understand how to compute the initial condition. Am I supposed to compute the initial by multiplying the original A by x(0) and then compute the matrix exponential for the new A? Or multiple e^(A) by x(0)? My notes aren't very clear. But those are my only guesses..

Thanks for any help.

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