IF i have a T-invariant subspaceU with dim$\displaystyle \geq 3$ containing the vector

v=

| -2 4 |

| 4 -2 |

with basis B=

| 1 0 |, | 1 1 |, | 1 1 |, | 1 1 |

| 0 0 | | 0 0 | | 0 1 | | 1 1 |

And $\displaystyle M_B(T)$ =

| 7 8 2 -8 |

|-3 -4 -2 8 |

|-3 -6 -5 -5 |

| 1 1 5 12 |

And i need to find a basis for the T-invariant subspace, how do i approach this..

Ive been trying to find T(u)..

but i dont know where im screwing up.. ive been using this.. $\displaystyle C_B(T(u))=M_B(T)C_B(u)$ to get to T(u)

witt $\displaystyle C_b(u)=$

| a+ b +c +d|

| b+c+d |

| d |

| c+ d |