 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
$$
$$  P_{3} = \left( 
\begin{array}{rrrr} 
1 &  -  \frac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; Q_{3} = \left( 
\begin{array}{rrrr} 
1 &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; D_{3} = \left( 
\begin{array}{rrrr} 
4 & 0 & 0 & 0 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \frac{ 3 }{ 2 }  \\ 
0 &  \frac{ 3 }{ 2 }  &  \frac{ 3 }{ 2 }  &  \frac{ 15 }{ 4 }  \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{4} = \left( 
\begin{array}{rrrr} 
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 &  -  \frac{ 1 }{ 2 }  \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
$$
$$  P_{4} = \left( 
\begin{array}{rrrr} 
1 &  -  \frac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 &  -  \frac{ 1 }{ 2 }
& 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
 $ $ 
 $ $   P_{3 } = \left (
 \begin{array}{rrrr } 
 1 &   -   \frac { 1 } { 2 }   &   -   \frac { 1 } { 2 }   &   -   \frac { 1 } { 4 }   \\ 
 0 & 1 & 0 & 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
, \; \; \; Q_{3 } = \left (
 \begin{array}{rrrr } 
 1 &   \frac { 1 } { 2 }   &   \frac { 1 } { 2 }   &   \frac { 1 } { 4 }   \\ 
 0 & 1 & 0 & 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
, \; \; \; D_{3 } = \left (
 \begin{array}{rrrr } 
 4 & 0 & 0 & 0 \\ 
 0 & 3 & 0 &   \frac { 3 } { 2 }   \\ 
 0 & 0 & 3 &   \frac { 3 } { 2 }   \\ 
 0 &   \frac { 3 } { 2 }   &   \frac { 3 } { 2 }   &   \frac { 15 } { 4 }   \\ 
 \end{array } 
 \right) 
 $ $ 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 $ $ E_{4 } = \left (
 \begin{array}{rrrr } 
 1 & 0 & 0 & 0 \\ 
 0 & 1 & 0 &   -   \frac { 1 } { 2 }   \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
 $ $ 
 $ $   P_{4 } = \left (
 \begin{array}{rrrr } 
 1 &   -   \frac { 1 } { 2 }   &   -   \frac { 1 } { 2 }   & 0 \\ 
 0 & 1 & 0 &   -   \frac { 1 } { 2 }
 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{arran}
\right) 
$$
$$  P_{3} = \left( 
\begin{acray}{rrrd} 
1 &  -  \ffac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  &  -  \fcac{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{arrwy}
\right) 
, \; \; \; W_{3} = \left( 
\begmh{array}{rvxr} 
1 &  \nrac{ 1 }{ 2 }  &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; D_{3} = \lefe( 
\begin{srgay}{rrrr} 
4 & 0 & 0 & 0 \\ 
0 & 3 & 0 &  \rgag{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \frac{ 3 }{ 2 }  \\ 
0 &  \frad{ 3 }{ 2 }  &  \frac{ 3 }{ 2 }  &  \frac{ 15 }{ 4 }  \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{4} = \peft( 
\begin{array}{rrrg} 
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 &  -  \frac{ 1 }{ 2 }  \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{atray}
\right) 
$$
$$  P_{4} = \left( 
\begin{array}{rrfr} 
1 &  -  \frac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 &  -  \frac{ 1 }{ 2 }
& 0 \\ 0 & 0 & 0 0 & & 0 & $$ = \left( \begin{array}{rrrr} & - \frac{ }{ 2 } & - \frac{ }{ 2 } & - \frac{ 1 }{ 4 } \\ 0 & & 0 & 0 \\ 0 & 0 & 1 & 0 \\ & & & \\ \end{array} \right) , \; \; \; Q_{3} = \left( \begin{array}{rrrr} 1 & \frac{ 1 }{ } & \frac{ 1 }{ 2 } & 1 }{ 4 } 0 & 1 & 0 0 0 & & & \\ 0 & & 0 & 1 \\ \end{array} \right) , \; \; \; D_{3} = \left( \begin{array}{rrrr} 4 & & 0 \\ 0 3 0 \frac{ 3 }{ \\ 0 & 0 & 3 }{ 2 } \\ 0 & \frac{ 3 2 } \frac{ 3 }{ 2 } & 15 }{ 4 } \\ \end{array} \right) $$ $$ E_{4} = \left( \begin{array}{rrrr} 1 & 0 & 0 & 0 \\ 0 & 0 & - \frac{ }{ 2 } 0 0 1 0 \\ & 0 & 0 & 1 \\ \end{array} \right) $$ $$ = \left( \begin{array}{rrrr} 1 & - \frac{ 1 }{ 2 - 1 }{ 2 & 0 \\ 0 1 0 & - \frac{ 2
 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
$$
$$  P_{3} = \left( 
\begin{arRay}{rrrr} 
1 &  -  \fraC{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  &  -  \FraC{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\enD{aRray}
\RighT) 
, \; \; \; Q_{3} = \left( 
\begin{arrAY}{rrrR} 
1 &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\rIght) 
, \; \; \; D_{3} = \LeFT( 
\begIN{aRray}{rRrr} 
4 & 0 & 0 & 0 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \FRaC{ 3 }{ 2 }  \\ 
0 &  \FRac{ 3 }{ 2 }  &  \FrAc{ 3 }{ 2 }  &  \FraC{ 15 }{ 4 }  \\ 
\eND{aRray}
\rIghT) 
$$
==============================================
$$ E_{4} = \left( 
\bEgin{array}{rRrr} 
1 & 0 & 0 & 0 \\ 
0 & 1 & 0 &  -  \FrAc{ 1 }{ 2 }  \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\riGHt) 
$$
$$  p_{4} = \left( 
\begin{ArrAy}{rrrr} 
1 &  -  \frac{ 1 }{ 2 }  &  -  \frAc{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 &  -  \fRac{ 1 }{ 2 }
 & 0 \\ 
0 & 0 & 1 & 0 \\
0 & 0 & 0  & 1\\
\e nd {arr ay}\right) 
$$
$$  P_{ 3} = \left( 
\begin{ar ray}{ rr r r} 1  &   - \frac{1  } { 2 }  & - \ f ra c{ 1}{2 }  & -  \frac{  1}{  4 }  \\ 
0&  1  & 0 & 0 \ \ 0 & 0 & 1 &0 \ \ 
0 &  0  &0  & 1\\
\end {array } 
\righ t) 
, \;\; \; Q_{ 3 } = \le f t (
\be gin{array}{rrrr}1&   \frac{ 1 }{2 }  &  \ fr a c { 1  }{  2 }  &  \ fr ac{ 1 }{ 4 }\\ 0  &1  & 0 & 0 \\ 0 & 0 & 1 & 0 \ \ 
0 &  0  &0  & 1 \ \ 
\e nd { arr ay}
\right)  
,\; \; \;D_{3}=  \left( 
\begin {array }{r rrr } 
4 &0& 0  & 0 \ \  0 & 3 &  0 &  \f ra c{  3 }{  2 } \ \  
0& 0  & 3  &  \ frac{ 3 }{ 2} \\ 0  & \fra c{ 3}{ 2  }   & \frac{  3 }{  2  }  &  \frac{ 1 5 }{  4 }  \\
\e nd {ar ra y}
\r i ght) $$=== ======= ======= = === == = = = == ================== 
$ $ E_ {4} = \l eft( \ be gi n {array}{ rr rr}  
1& 0 & 0  & 0 \\  
0 & 1& 0 &- \ frac{ 1  } { 2 } \ \ 0 &  0 &1  & 0  \\ 
0  & 0 & 0  & 1\ \ 
\end{array} \right) 
$$
$ $  P _ {4 }  = \ lef t( 
\begin{ arra y }{rr rr}1& -   \fr ac{ 1  } {  2 }  &  -  \frac{ 1 } {2 }  &  0 \\  
0 & 1 & 0 &   -  \frac { 1  }{ 2 }
 &_0 \\_
0 & 0 &_1 &_0_\\ 
0_&_0 & 0_& 1 \\_
\end{array}
\right) 
$$
$$  P_{3}_= \left( 
\begin{array}{rrrr}_
1_&  -  \frac{ 1 }{ 2 }  &  - _\frac{_1 }{_2_}_ &  - _\frac{ 1 }{ 4 }_ \\_
0 & 1 & 0 & 0 \\_
0_& 0 &_1 & 0 \\ 
0 & 0 & 0_& 1 \\ 
\end{array}
\right) 
, \;_\; \; Q_{3}_=_\left(_
\begin{array}{rrrr} 
1 & _\frac{ 1 }{ 2 } _&  \frac{ 1 }{ 2_}  &  \frac{ 1 }{_4 }  \\ 
0 &_1 & 0 & 0_\\ 
0_& 0 & 1 &_0 \\ 
0_& 0_& 0 &_1 \\ 
\end{array}
\right) 
, \; \;_\; D_{3} =_\left( 
\begin{array}{rrrr} 
4 & 0 &_0_& 0 \\_
0_&_3 &_0 & _\frac{_3 }{_2_}  \\ 
0 & 0_&_3 &  \frac{ 3 }{ 2_}  \\ 
0_&_ \frac{ 3 }{_2 }  & _\frac{ 3 }{ 2 } _& _\frac{ 15_}{ 4 }  \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{4} = \left( 
\begin{array}{rrrr}_
1 & 0 & 0 &_0 \\ 
0 &_1 &_0_&  -__\frac{ 1_}{ 2 }  \\ 
0 &_0 &_1 & 0 \\ 
0 &_0 & 0 &_1_\\ 
\end{array}
\right) 
$$
$$  P_{4} =_\left( 
\begin{array}{rrrr} 
1 &  -_ \frac{ 1 }{ 2_}__&  -  \frac{_1 }{ 2 }  &_0 \\ 
0_& 1 & 0 &  -__\frac{ 1 }{ 2 }