Multivariate Calculus question

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mckallin
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Hi, could anyone tell me the steps to solve the following question:

Find the solution of x'=Ax with the initial value

-------1---------2 0 0
x(0)=( 0 ), if A=( 0 1 -1 )
-------1---------1 1 1
 
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Don't you want to start by finding the eigenvectors and eigenvalues of A?