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Determine e At by first finding a fundamental matrix X(t) for x = Ax and then using the formula eAt = X(t)X(0)1. 0 2 2 2 0 2

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fundamental naatix xfor AX and us the X(t). Xl0) 2 A= 2 2 find jeneral solation far X=AX find egenvalues of As Thus So fixstHence eigen-values of matrix A and the -2 4 are Next we find eanvectoY carresPondin eigenvalua dz to For 4 (A-47) -4 2 4 2 22-2 (A+21uo O 2 2 2 2- 2 2a + 23,_+ 243. 92 -1 Let a 9 then ay +911 LetaHence general solution of l AX Xtt et (+)X (stett Ths 요ves a fundamantal matix solution ett e-2t -2t -e-24 X) - 2/3X plug in the formula e e-at e e 31 3 -2t 9 3

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