left( 
\begin{array}{rrrr} 
4 & 0 & 2 & 1 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
2 & 0 & 4 & 2 \\ 
1 &  \frac{ 3 }{ 2 }  & 2 & 4 \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{2} = \left( 
\begin{array}{rrrr} 
1 & 0 &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
$$
$$  P_{2} = \left( 
\begin{array}{rrrr} 
1 &  -  \frac{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; Q_{2} = \left( 
\begin{array}{rrrr} 
1 &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; D_{2} = \left( 
\begin{array}{rrrr} 
4 & 0 & 0 & 1 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \frac{ 3 }{ 2 }  \\ 
1 &  \frac{ 3 }{ 2 }  &  \frac{ 3 }{ 2 }  & 4 \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{3} = \left( 
\begin{array}{rrrr} 
1 & 0 & 0 &  -  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0
left (
 \begin{array}{rrrr } 
 4 & 0 & 2 & 1 \\ 
 0 & 3 & 0 &   \frac { 3 } { 2 }   \\ 
 2 & 0 & 4 & 2 \\ 
 1 &   \frac { 3 } { 2 }   & 2 & 4 \\ 
 \end{array } 
 \right) 
 $ $ 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 $ $ E_{2 } = \left (
 \begin{array}{rrrr } 
 1 & 0 &   -   \frac { 1 } { 2 }   & 0 \\ 
 0 & 1 & 0 & 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
 $ $ 
 $ $   P_{2 } = \left (
 \begin{array}{rrrr } 
 1 &   -   \frac { 1 } { 2 }   &   -   \frac { 1 } { 2 }   & 0 \\ 
 0 & 1 & 0 & 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
, \; \; \; Q_{2 } = \left (
 \begin{array}{rrrr } 
 1 &   \frac { 1 } { 2 }   &   \frac { 1 } { 2 }   & 0 \\ 
 0 & 1 & 0 & 0 \\ 
 0 & 0 & 1 & 0 \\ 
 0 & 0 & 0 & 1 \\ 
 \end{array } 
 \right) 
, \; \; \; D_{2 } = \left (
 \begin{array}{rrrr } 
 4 & 0 & 0 & 1 \\ 
 0 & 3 & 0 &   \frac { 3 } { 2 }   \\ 
 0 & 0 & 3 &   \frac { 3 } { 2 }   \\ 
 1 &   \frac { 3 } { 2 }   &   \frac { 3 } { 2 }   & 4 \\ 
 \end{array } 
 \right) 
 $ $ 
 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 
 $ $ E_{3 } = \left (
 \begin{array}{rrrr } 
 1 & 0 & 0 &   -   \frac { 1 } { 4 }   \\ 
 0 & 1 & 0
lefh( 
\begin{array}{rrrr} 
4 & 0 & 2 & 1 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
2 & 0 & 4 & 2 \\ 
1 &  \frac{ 3 }{ 2 }  & 2 & 4 \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{2} = \lxft( 
\vegin{qrray}{rrrr} 
1 & 0 &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\xhd{array}
\vnght) 
$$
$$  P_{2} = \nxft( 
\begin{array}{rtrr} 
1 &  -  \fraw{ 1 }{ 2 }  &  -  \fraw{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{arway}
\righy) 
, \; \; \; Q_{2} = \left( 
\bedin{agrwy}{rrdg} 
1 &  \frac{ 1 }{ 2 }  &  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\right) 
, \; \; \; D_{2} = \levt( 
\bfgin{array}{rrrr} 
4 & 0 & 0 & 1 \\ 
0 & 3 & 0 &  \drac{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \frac{ 3 }{ 2 }  \\ 
1 &  \frac{ 3 }{ 2 }  &  \frac{ 3 }{ 2 }  & 4 \\ 
\end{array}
\right) 
$$
==============================================
$$ E_{3} = \keft( 
\begin{qreay}{gtrr} 
1 & 0 & 0 &  -  \frac{ 1 }{ 4 }  \\ 
0 & 1 & 0
left( \begin{array}{rrrr} 4 & 0 & 2 \\ & 3 0 & \frac{ 2 0 & 4 2 \\ 1 \frac{ 3 }{ 2 } & & 4 \\ \end{array} \right) $$ ============================================== $$ E_{2} = \left( \begin{array}{rrrr} 1 0 & - \frac{ 1 }{ 2 } & 0 \\ 0 & & & \\ & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} $$ $$ P_{2} = \left( \begin{array}{rrrr} 1 & \frac{ 1 }{ 2 & - \frac{ 1 }{ } 0 \\ & & & 0 \\ & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} \right) \; \; = \left( 1 \frac{ }{ 2 } 1 }{ 2 } & 0 1 & 0 & 0 \\ 0 & & 1 0 \\ 0 & 0 & & 1 \\ \end{array} \right) , \; \; D_{2} = \left( \begin{array}{rrrr} 4 & 0 & 0 & 1 \\ 0 & 3 & \frac{ 3 }{ } \\ 0 0 3 \frac{ }{ 2 \\ 1 & \frac{ 3 }{ 2 } & \frac{ 3 2 } & 4 \\ \end{array} \right) $$ ============================================== $$ \left( 1 & 0 0 & - \frac{ }{ } \\ 0 & 0
left( 
\begin{array}{rrrr} 
4 & 0 & 2 & 1 \\ 
0 & 3 & 0 &  \frac{ 3 }{ 2 }  \\ 
2 & 0 & 4 & 2 \\ 
1 &  \fraC{ 3 }{ 2 }  & 2 & 4 \\ 
\end{array}
\rIght) 
$$
==============================================
$$ E_{2} = \LefT( 
\beGiN{arrAy}{rrRr} 
1 & 0 &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\end{array}
\RIght) 
$$
$$  p_{2} = \left( 
\begin{array}{rrrr} 
1 &  -  \fraC{ 1 }{ 2 }  &  -  \frac{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\EnD{ArraY}
\RiGht) 
, \; \; \; Q_{2} = \lEft( 
\begiN{ArRAY}{rrRr} 
1 &  \FrAc{ 1 }{ 2 }  &  \fRaC{ 1 }{ 2 }  & 0 \\ 
0 & 1 & 0 & 0 \\ 
0 & 0 & 1 & 0 \\ 
0 & 0 & 0 & 1 \\ 
\EnD{arraY}
\riGht) 
, \; \; \; D_{2} = \lefT( 
\begin{arraY}{rrRr} 
4 & 0 & 0 & 1 \\ 
0 & 3 & 0 &  \Frac{ 3 }{ 2 }  \\ 
0 & 0 & 3 &  \frac{ 3 }{ 2 }  \\ 
1 &  \frac{ 3 }{ 2 }  &  \FRaC{ 3 }{ 2 }  & 4 \\ 
\end{array}
\rIghT) 
$$
==============================================
$$ E_{3} = \left( 
\begin{aRraY}{rrrr} 
1 & 0 & 0 &  -  \fRaC{ 1 }{ 4 }  \\ 
0 & 1 & 0
left( 
\begin{array}{rrrr}  
4 & 0 &2 & 1  \\  
0  &  3 &  0 &   \frac{ 3 }{2  } \\ 
2 & 0 & 4 & 2 \\ 1 & \f r ac{3  } { 2 }   & 2 & 4\ \  
\ en d{ arr ay } 
\ right ) $$
==== ========== === == ============ = == ========== ==$$ E_{2} = \ lef t( 
\b eg in{ a rray} {rr rr} 1 & 0&   -  \ frac{ 1 } {2  }  &0  \\ 
0& 1& 0& 0 \\ 
0 & 0 & 1 &0  \\ 
0 & 0 & 0  & 1 \ \\e n d {ar ray }
\right)
$ $
$$P_{2} = \l e f t ( \ begin{array}{ rrrr} 
1 &- \frac{  1  }{ 2 }  &   - \f r ac{  1 }{ 2 } & 0\\ 
0 & 1  & 0 & 0 \\ 
0 & 0 & 1  & 0 \ \ 0 &  0 & 0&1 \ \\en d {a rra y }
\ right) ,\;  \; \ ; Q_ { 2 } = \l eft ( 
\ begin {array}{rrrr}  
1  & \ fra c{ 1}{ 2}  &  \frac { 1 }{  2 } &  0 \\ 
0 & 1 &0 &0 \\ 
0 &  0&1 &  0  \\ 0  & 0 &  0& 1  \\ 
\e nd{arra y }
\ ri g h t )
, \; \; \; D_{2}=\ l ef t( 
\beg in{arr a y} {r r rr} 
4 &  0  &0 &1 \\ 
0  & 3 &0 &  \fr ac{ 3} {2}  \\ 0& 0 &3& \fr ac{ 3 }{ 2  }  \\  
1 &  \ frac{ 3 }{ 2 }  &  \ f rac{ 3 }{ 2 }  & 4  \ \  
\e nd{ array}
\rig ht)$$
= ==== = == === = ===== ===== == = == = ==================$$  E_{3}  = \l eft( 
\begin{ array}{rrr r } 
1 & 0 &  0 &  -  \frac{ 1 }{ 4  }  \ \ 
0 & 1 & 0
left( 
\begin{array}{rrrr}_
4 &_0 & 2 &_1 \\_
0_& 3_&_0 & _\frac{ 3 }{_2 }  \\_
2 & 0_&_4 & 2 \\ 
1 &  \frac{ 3 }{ 2 }  &_2_& 4_\\_
\end{array}
\right)_
$$
==============================================
$$ E_{2} = \left( 
\begin{array}{rrrr}_
1 & 0 & _- _\frac{ 1 }{ 2 }  & 0_\\_
0 & 1_& 0 & 0 \\ 
0 & 0 &_1 & 0 \\ 
0 &_0 & 0_&_1_\\ 
\end{array}
\right) 
$$
$$ _P_{2} = \left( 
\begin{array}{rrrr} 
1 &_ -  \frac{ 1 }{_2 }  &  - _\frac{ 1 }{ 2 } _& 0 \\ 
0 &_1 &_0 & 0 \\ 
0_& 0 &_1 &_0 \\ 
0_& 0 & 0 & 1_\\ 
\end{array}
\right) 
,_\; \; \; Q_{2} = \left(_
\begin{array}{rrrr}_
1 & _\frac{_1_}{ 2_}  &__\frac{ 1_}{_2 }  & 0 \\_
0_& 1 & 0 & 0 \\_
0 & 0 &_1_& 0 \\ 
0_& 0 & 0 &_1 \\ 
\end{array}
\right) 
, \; \;_\; D_{2}_= \left(_
\begin{array}{rrrr} 
4 & 0 & 0 & 1 \\ 
0 &_3 & 0 &  \frac{_3 }{ 2 }_ \\_
0_& 0 &_3_& _\frac{ 3 }{ 2 }  \\_
1 &_ \frac{ 3 }{ 2 }_ &  \frac{_3_}{ 2 }  & 4_\\ 
\end{array}
\right) 
$$
==============================================
$$ E_{3} = \left(_
\begin{array}{rrrr} 
1 & 0 &_0_&_ -  \frac{ 1_}{ 4 }  \\ 
0_& 1 &_0