HW 1 laudari sudip

 $$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrr}
1 & 2 & 1 & 2 & 1 & 2 & 4 \\
0 & 1 & 1 & 0 & 0 & 1 & 0 \\
2 & 0 & 0 & 1 & 1 & 2 & 0 \\
1 & 0 & 1 & 2 & 4 & 0 & 0 \\
1 & 1 & 2 & 0 & 0 & 1 & 1 \\
1 & 1 & 6 & 3 & 0 & 1 & 0 \\
1 & 1 & 3 & -1 & 1 & 1 & 0
\end{array}\right)$$ 

 $$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrr}
0 & 1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 & 0 & 0
\end{array}\right)$$ 
 $$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrr}
1 & 0 & 0 & 0 & 0 & 0 & 0 \\
\frac{1}{2} & 1 & 0 & 0 & 0 & 0 & 0 \\
\frac{1}{2} & \frac{1}{2} & 1 & 0 & 0 & 0 & 0 \\
\frac{1}{2} & \frac{1}{2} & \frac{5}{11} & 1 & 0 & 0 & 0 \\
\frac{1}{2} & 0 & \frac{2}{11} & -\frac{26}{67} & 1 & 0 & 0 \\
0 & \frac{1}{2} & \frac{1}{11} & \frac{20}{67} & -\frac{24}{259} & 1 & 0 \\
\frac{1}{2} & \frac{1}{2} & \frac{3}{11} & \frac{38}{67} & -\frac{59}{259} & -\frac{19}{23} & 1
\end{array}\right)$$ 
 $$\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrr}
2 & 0 & 0 & 1 & 1 & 2 & 0 \\
0 & 2 & 1 & \frac{3}{2} & \frac{1}{2} & 1 & 4 \\
0 & 0 & \frac{11}{2} & \frac{7}{4} & -\frac{3}{4} & -\frac{1}{2} & -2 \\
0 & 0 & 0 & -\frac{67}{22} & \frac{13}{22} & -\frac{3}{11} & -\frac{12}{11} \\
0 & 0 & 0 & 0 & \frac{259}{67} & -\frac{68}{67} & -\frac{4}{67} \\
0 & 0 & 0 & 0 & 0 & \frac{138}{259} & -\frac{388}{259} \\
0 & 0 & 0 & 0 & 0 & 0 & -\frac{25}{23}
\end{array}\right)$$ 

[  24/5]
[ 77/15]
[     0]
[ -4/15]
[ -1/15]
[-47/15]
[  -9/5]

True