Chapter 5 - Eigenvalues and Eigenvectors - 5.2 Exercises - Page 281: 1

Characteristic polynomial: $\lambda^2-4\lambda -45$ $\lambda = -5, 9$

1.) To find the characteristic polynomial, find $det(A-\lambda I)$ $=(2-\lambda)(2-\lambda)-49$ $=\lambda^2-4\lambda-45$ 2.) Solve for the eigenvalues by equating the characteristic equation to zero and solving for $\lambda$ $\lambda^2-4\lambda-45=0$ $(\lambda+5)(\lambda-9) = 0$ $\lambda=-5,9$