<s>[INST] set G equal to what? 
My attempts :  i construct a matrix  $A= \begin{bmatrix} 1&0&0&0&0&0&0&0\\ 0&1&0&0&0&0&0&0\\ 0&0&2&1&0&0&0&0\\ 0&0&0&2&0&0&0&0\\ 0&0&0&0&2&0&0&0\\ 0&0&0&0&0&2&0&0\\ 0&0&0&0&0&0&2&0\\ 0&0&0&0&0&0&0&2\end{bmatrix}$
Now  we know that the characteristic polynomial of A is $(x − 1)^2
(x − 2)^6$
and the minimal polynomial of A is$ (x − 1)(x − 2)^2$  
Now we will  take  only eigenvalue $ 2$  of $ A$  that  is  characteristic  of eigenvalue $2  =(x-2)^6$ and the minimial of eigenvalue $2 = (x-1)^2$
Now  set  G will   be    equal to  $ 6- 2 = 4$
so  $G = 4$
Is  my answer is correct or nots?  pliz reply 
i  have  my exam tommorrows. so  i need its  urgently   any Hints/solution 
Thanks in advance   i would be more thankful
 [/INST] In the matrix $A$ we have an eigenvalue $2$ which has geometric multiplicity $4$ and one which has geometric multiplicity $1$ (the one of the jordan block $2-by-2$). Thus we have that $G=\{1,4\}$.
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