Solve the following system of first-order initial-value problems via eigenvalues and eigenvectors: dx dt dx dt...

 

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Solve the following system of first-order initial-value problems via eigenvalues and eigenvectors: dx₁ dt dx₂ dt = X₁ - 2X₂ X3; x₁ (0) = 1 = -X₁ + X₂ + x3; X₂ (0) = 0 dx3 dt = X₁ X3 X3 (0) = -2 Solve the following system of first-order initial-value problems via eigenvalues and eigenvectors: dx₁ dt dx₂ dt = X₁ - 2X₂ X3; x₁ (0) = 1 = -X₁ + X₂ + x3; X₂ (0) = 0 dx3 dt = X₁ X3 X3 (0) = -2