(Solved): Find the eigenvalues of the given matrix. Enter your answers from smallest eigenvalue to the large ...

Find the eigenvalues of the given matrix. Enter your answers from smallest eigenvalue to the largest eigenvalue. For repeated eigenvalues, enter the value as many times as needed. If the number of eigenvalues is lower than 3 , enter NONE in the unused fields. \[ \left(\begin{array}{rrr} 0 & 25 & 0 \\ -1 & -10 & 0 \\ 0 & 0 & -5 \end{array}\right) \] \[ \begin{array}{l} \lambda_{1}= \\ \lambda_{2}= \\ \lambda_{3}= \end{array} \] Find the corresponding eigenvectors. Enter NONE for unused fields. Note that one of the elements of the eigenvectors is given. \[ \mathrm{K}_{1}= \] \[ \mathrm{K}_{2}= \] 1 \[ \mathrm{K}_{3}= \] State whether the given matrix is singular or nonsingular by considering the following theorem: "A matrix \( \mathbf{A} \) is singular if and only if the number 0 is an eigenvalue of \( \mathbf{A} . " \)