(1 point) Consider the initial value problem a. Find the eigenvalue X, an eigenvector , and...

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(1 point) Consider the initial value problem a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector ₂ for the coefficient matrix of this linear system. TE X= Y₂ (t) = = c. Solve the original initial value problem. y₁ (t) = y y(t) = C₁ -5 = [ |ū, ÿ(0) = || 0 -5 7₁ = [3³]. b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. +c S 1 V₂ = (1 point) Consider the initial value problem a. Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector ₂ for the coefficient matrix of this linear system. TE X= Y₂ (t) = = c. Solve the original initial value problem. y₁ (t) = y y(t) = C₁ -5 = [ |ū, ÿ(0) = || 0 -5 7₁ = [3³]. b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. +c S 1 V₂ =