For the given matrix $A$

$A=\left[\begin{array}{ccc}1& 3& 4\\ 3& 1& 2\\ 4& 2& 1\end{array}\right]$

Write QR algonthm code to perform QR iteration on above matrix $A$ as described in lecture. Show that after about $20$ iteration $($i$.$e$.k=20),$ you receive $A_{20}$ as below:

$A_{20}=\left[\begin{array}{ccc}7\mathrm{.}074& 0& 0\\ 0& -3\mathrm{.}187& 0\\ 0& 0& -0\mathrm{.}886\end{array}\right]$

To receive the QR factorization at each iteration, you may use any function available e$.$g$.$ Gram$-$Schmidt method in Python.