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Let A = 2 4 -2 (a) Find the characteristic polynomial of A p(x) = (b) Find the eigenvalues of A and bases for the associated eigenspaces: Smallest elgenvalue Basis for the associated elgenspace: { Largest elgenvalue Basis for the associated elgenspace: }

Let A = 2 4 -2 (a) Find the characteristic polynomial of A p(x) = (b) Find the eigenvalues of A and bases for the associated eigenspaces: Smallest elgenvalue Basis for the associated elgenspace: { Largest elgenvalue Basis for the associated elgenspace: }

Advanced Engineering Mathematics
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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### Linear Algebra Example: Eigenvalues and Eigenvectors Given the matrix: \[ A = \begin{bmatrix} 2 & 4 \\ 0 & -2 \end{bmatrix} \] #### (a) Find the characteristic polynomial of \( A \) \[ p(x) = \, \] *(Box where students can input the characteristic polynomial equation)* #### (b) Find the eigenvalues of \( A \) and bases for the associated eigenspaces: - **Smallest eigenvalue** \[ \boxed{} \] Basis for the associated eigenspace: \[ \boxed{} \] - **Largest eigenvalue** \[ \boxed{} \] Basis for the associated eigenspace: \[ \boxed{} \] This exercise guides students through finding the characteristic polynomial, eigenvalues, and associated eigenspaces of a given matrix \( A \).
Transcribed Image Text:### Linear Algebra Example: Eigenvalues and Eigenvectors Given the matrix: \[ A = \begin{bmatrix} 2 & 4 \\ 0 & -2 \end{bmatrix} \] #### (a) Find the characteristic polynomial of \( A \) \[ p(x) = \, \] *(Box where students can input the characteristic polynomial equation)* #### (b) Find the eigenvalues of \( A \) and bases for the associated eigenspaces: - **Smallest eigenvalue** \[ \boxed{} \] Basis for the associated eigenspace: \[ \boxed{} \] - **Largest eigenvalue** \[ \boxed{} \] Basis for the associated eigenspace: \[ \boxed{} \] This exercise guides students through finding the characteristic polynomial, eigenvalues, and associated eigenspaces of a given matrix \( A \).
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