and 
are defined in the following manner:
then find the value of 
then find the value of 
and ![$e\in [-2,2]$](http://latex.artofproblemsolving.com/b/b/7/bb78c9dedb18af5e6a904f5492917921e41a7ebc.png)
such that 
Find the value of 
matrix 
,
is the matrix of all ones?
be a function, two times derivable on 
for which there exist 
such that![\[ \frac { f(b)-f(a) }{b-a} \neq f'(c) ,\]](http://latex.artofproblemsolving.com/a/3/1/a31861ef909a6e17ed8b495b9b9b16d887ba573f.png)
for all 
.
.
Find the maximum positive integer 
such that for every subset 
with n elements, there always exist two elements a, b in T such that:
Y by
Let 
be a positive integer, and 
be two complex numbers such that 
and 
, for any 
. The matrices 
satisfy the relation 
. Prove that 
and 
are invertible.
be a positive integer, and 
be two complex numbers such that 
and 
, for any 
. The matrices 
satisfy the relation 
. Prove that 
and 
are invertible.
