題組內容

7. Give two matrices \( [A] = \begin{bmatrix} 1 & 3 & 5 \\ 2 & 4 & 4 \\ 1 & -1 & 1 \end{bmatrix} ; [B] = \begin{bmatrix} 5 & -1 & 0 \\ 0 & -5 & 9 \\ 5 & -1 & 0 \end{bmatrix} \).

(b) Find all the eigenvalues and their corresponding eigenvectors of [B]. (10%)