1.4.46 Matrix transformations

condition: Determine the algebraic and geometric multiplicities of a multiple eigenvalue: \[ \left(\begin{array}{ccc} -11 & 3 & -6 \\ 0 & -1 & 0 \\ 20 & -5 & 11 \end{array}\right) \] eigenvalues given: \( -1,-1,1 \).