(Solved): Find the eigenvalues and number of independent eigenvectors. (Hint: 1 is an eigenvalue.) \[ \left[\ ...

Find the eigenvalues and number of independent eigenvectors. (Hint: 1 is an eigenvalue.) \[ \left[\begin{array}{lll} 5 & -2 & 0 \\ 4 & -1 & 0 \\ 4 & -4 & 3 \end{array}\right] \] a) Eigenvalues: \( 1,-1,3 \); Number of independent eigenvectors: 2 b) Eigenvalues: \( 1,-3,3 \); Number of independent eigenvectors: 3 c) Eigenvalues: \( 1,-3,-3 \); Number of independent eigenvectors: 2 d) Eigenvalues: 1,3,3; Number of independent eigenvectors: 3 e) Eigenvalues: \( 1,3,3 \); Number of independent eigenvectors: 2 f) None of the above.