Considere o determinante de uma matriz de ordem n definido por:

!$ \Delta_n \, = \, \begin {vmatrix} 1 \,\,\,\,\,\,\,\, 1 \,\,\,\,\,\,\,\, 1 \,\,\,\,\,\,\,\, 1 \,\,\,\,\, ... \,\,\,\,\, 1 \,\,\,\,\, 1 \\ -1 \,\,\,\,\, 3 \,\,\,\,\, 0 \,\,\,\,\, 0 \,\,\,\,\, ... \,\,\,\,\, 0 \,\,\,\,\, 0 \\ 0 \,\,\,\,\, -1 \,\,\,\,\, 3 \,\,\,\,\, 0 \,\,\,\,\, ... \,\,\,\,\, 0 \,\,\,\,\, 0 \\ 0 \,\,\,\,\, 0 \,\,\,\,\, -1 \,\,\,\,\, 3 \,\,\,\,\, ... \,\,\,\,\, 0 \,\,\,\,\, 0 \\ ......................... \\ 0 \,\,\,\,\, 0 \,\,\,\,\, 0 \,\,\,\,\, 0 \,\,\,\,\, ... \,\,\,\,\, 3 \,\,\,\,\, 0 \\ 0 \,\,\,\,\, 0 \,\,\,\,\, 0 \,\,\,\,\, 0 \,\,\,\,\, ... \,\,\,\,\, -1 \,\,\,\,\, 3 \end {vmatrix} !$

Sabendo que !$ \Delta_1 \, = \, 1, !$ o valor de !$ \Delta_{10} !$ é