Consider the matrix $D=\left[\begin{array}{ccc}1& 0& 1\\ 1& -1& 2\\ 2& -1& 3\end{array}\right].$

$($a$)$ Use MATLAB to solve the matrix equation $Dx=0.$

$($b$)$ Enter the following into the Command Window:

null$($D$,$"rational"$)$

Compare the output of this code to your answer in part $($a$).$

$($c$)$ Now define a $35$ matrix $M$ and solve the system $Mx=0,$ writing your answer in parametric vector form. Perform the following command,

null $($M$,$ "rational"$)$

Compare your solution to $Mx=0$ with the output of this command. What do you think this command does? $($You may want to try this with several different choices of M$.)$