The matrix $A = \begin{pmatrix} 4 & 2 \\ 2 & 1 \end{pmatrix}$ has eigenvalues $\lambda_1$ and $\lambda_2$. If $\lambda_1 > \lambda_2$, what is the value of $\lambda_1$?

Answer Key:

5

### Solution: Characteristic equation: $\det(A - \lambda I) = (4 - \lambda)(1 - \lambda) - 4 = \lambda^2 - 5\lambda = 0 \implies \lambda(\lambda - 5) = 0$. Eigenvalues are $5$ and $0$. Larger eigenvalue $\lambda_1 = 5$. Correct: 5.

← Prev Question Next Question →