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Hint: use the Euler identity ecos+isin 62. LetT0 0 1-3 2 0eigenvector. For the complex conjugate eigenvalues, construct a complex eigen-(a) Find the eigenvalues for the matrix A. For the real eigenvalue, compute a realvector.Ax, and(b) Use (a) to compute a real fundamental matrix Φ(t) for the systern r,use Φ(t) to calculate the solution of this system that satisfies the initial condition

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pls explain to me step by step. thanks

Hint: use the Euler identity ecos
+isin 6
2. Let
T0 0 1
-3 2 0
eigenvector. For the complex conjugate eigenvalues, construct a complex eigen-
(a) Find the eigenvalues for the matrix A. For the real eigenvalue, compute a real
vector.
Ax, and
(b) Use (a) to compute a real fundamental matrix Φ(t) for the systern r,
use Φ(t) to calculate the solution of this system that satisfies the initial condition
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Hint: use the Euler identity ecos +isin 6 2. Let T0 0 1 -3 2 0 eigenvector. For the complex conjugate eigenvalues, construct a complex eigen- (a) Find the eigenvalues for the matrix A. For the real eigenvalue, compute a real vector. Ax, and (b) Use (a) to compute a real fundamental matrix Φ(t) for the systern r, use Φ(t) to calculate the solution of this system that satisfies the initial condition

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