Exercise · ZW-LINEAR-SYSTEM-AND-EIGENVALUES-001 · ★☆☆ Basic
What are the eigenvalues of \(A=\begin{pmatrix}1&2\\2&1\end{pmatrix}\)?
Choose one option.
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- C. \(3\) y \(-1\)
Explanation
\(\det(A-\lambda I)=(1-\lambda)^2-4=0\) gives \(1-\lambda=\pm2\), that is, \(\lambda=3\) or \(\lambda=-1\).
Review the concept: Linear system and eigenvalues
Homogeneous system with a constant \(n\times n\) matrix \(A\), whose elementary solutions are built from an eigenvalue \(\lambda\) and an eigenvector \(\mathbf v\) of \(A\).
\[\mathbf x'=A\mathbf x,\qquad \mathbf x(t)=e^{\lambda t}\mathbf v,\quad A\mathbf v=\lambda\mathbf v\]
More practice problems: linear system and eigenvalues
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