**Problem Statement**a. Find the eigenvalues and eigenvectors of the matrix \[\begin{bmatrix}5 & -3 \\4 & -2 \end{bmatrix}\]- Eigenvalue \( \lambda_1 = \underline{\hspace{2cm}} \), - Eigenvector \( \mathbf{v}_1 = \begin{bmatrix} \underline{\hspace{1cm}} \\ \underline{\hspace{1cm}} \end{bmatrix} \),- Eigenvalue \( \lambda_2 = \underline{\hspace{2cm}} \),- Eigenvector \( \mathbf{v}_2 = \begin{bmatrix} \underline{\hspace{1cm}} \\ \underline{\hspace{1cm}} \end{bmatrix} \)b. Solve the system of differential equations \[\mathbf{x}' = \begin{bmatrix} 5 & -3 \\ 4 & -2 \end{bmatrix} \mathbf{x}\]satisfying the initial conditions \[\begin{bmatrix}x_1(0) \\x_2(0)\end{bmatrix}=\begin{bmatrix}-2 \\-3\end{bmatrix}\]- Solution: - \( x_1(t) = \underline{\hspace{10cm}} \) - \( x_2(t) = \underline{\hspace{10cm}} \)

Answered: Image /qna-images/answer/cff939a1-161f-480e-9e07-877b641ed4f3.jpg

Answered: a. Find the eigenvalues and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a. Find the eigenvalues and eigenvectors of the matrix x₁ (t) x₂(t): = X₁ b. Solve the system of differential equations a' = = V₁ = 5 -3 [2] 4 -2 -3 = √²₁ -2] and X₂ = e satisfying the initial conditions V2 x₁ (0) =