(Solved): Find the eigenvalues and number of independent eigenvectors. \[ \left[\begin{array}{rrr} 0 & 1 & -2 ...

Find the eigenvalues and number of independent eigenvectors. \[ \left[\begin{array}{rrr} 0 & 1 & -2 \\ 2 & -1 & -2 \\ 6 & -2 & -3 \end{array}\right] \] a) Eigenvalues: \( -2,2+i, 2-i \); Number of independent eigenvectors: 3 b) Eigenvalues: \( 2,-1+2 i,-1-2 i \); Number of independent eigenvectors: 3 c) Eigenvalues: \( -1,2+i, 2-i \); Number of independent eigenvectors: 3 d) Eigenvalues: \( 1,-1+2 i,-1-2 i \); Number of independent eigenvectors: 3 e) Eigenvalues: \( -2,-1+2 i,-1-2 i \); Number of independent Eigenvectors: 3 f) None of the above.