Write a function that inputs a $44$ matrix $x.$ This function should output True if $x$ is

a transformation matrix and False if $x$ is not a transformation matrix. Demonstrate that

your function works with the following matrices:

$x_1=\left[\begin{array}{ccccccccccccc}\frac{1}{\sqrt[\phantom{2}]{2}}& -\frac{1}{\sqrt[\phantom{2}]{2}}& 0& -5& \frac{1}{\sqrt[\phantom{2}]{2}}& 0& -1\mathrm{.}7& 0& 1& -11& 0& 0& 1\end{array}\right]$

$0$

$0$

$0$

$0$

$0$

$\frac{1}{\sqrt[\phantom{2}]{2}},x_2=\left[\begin{array}{ccccccccccccc}0\mathrm{.}5& -\frac{1}{\sqrt[\phantom{2}]{2}}& 0\mathrm{.}5& 0& \frac{1}{\sqrt[\phantom{2}]{2}}& 0\mathrm{.}5& 0& 0& \frac{1}{\sqrt[\phantom{2}]{2}}& 0& 0& 1& 1\end{array}\right]$

$0$

$-\frac{1}{\sqrt[\phantom{2}]{2}}$

$0\mathrm{.}5$

$x_3=\left[\begin{array}{ccccccccccccc}-\frac{1}{\sqrt[\phantom{2}]{2}}& -0\mathrm{.}5& 0\mathrm{.}5& -1\mathrm{.}1& -0\mathrm{.}5& -0\mathrm{.}5& 4\mathrm{.}5& \frac{1}{\sqrt[\phantom{2}]{2}}& \frac{1}{\sqrt[\phantom{2}]{2}}& 1\mathrm{.}6& 0& 0& 1\end{array}\right]$

$0$

$0$

$\frac{1}{\sqrt[\phantom{2}]{2}}$