Linear Algebra

The characteristic equation of matrix $A$ is given by: $\det(A - \lambda I) = 0$ $\begin{vmatrix} 2 - \lambda & 1 \\ 1 & 2 - \lambda \end{vmatrix} = (2-\lambda)^2 - 1 = 0$ $\lambda^2 - 4\lambda + 3 = 0 \implies (\lambda - 3)(\lambda - 1) = 0$ The eigenvalues are $\lambda_1 = 3$ and $\lambda_2 = 1$. The maximum eigenvalue is $3$.