(Solved): Find all of the eigenvalues \( \lambda \) of the matrix \( A \). (Hint: Use the method of Example ...

Find all of the eigenvalues \( \lambda \) of the matrix \( A \). (Hint: Use the method of Example \( 4.5 \) of finding the solutions to the equation \( 0= \) det \( (A-\lambda I) \). Enter your answers as a comma-separated list.) \[ A=\left[\begin{array}{ll} 3 & 5 \\ 8 & 0 \end{array}\right] \] \[ \lambda= \] Give bases for each of the corresponding eigenspaces. \( \operatorname{span}([(])) \) (smaller \( \lambda \)-value) \( \operatorname{span}([(]))( \) (larger \( \lambda \)-value) Illustrate the eigenspaces and the effect of multiplying eigenvectors by \( A \) as in the figure below.