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

Question

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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Transcribed Image Text

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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