If $A=\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 6& 7& 8\end{array}\right],$ what is the X$\_$centered array?

If the covariance array of the $x\_$centered array is:

$\left[\begin{array}{ccc}6\mathrm{.}33& 4\mathrm{.}33& -3\mathrm{.}33\\ 4\mathrm{.}33& 7\mathrm{.}23& -5\mathrm{.}12\\ -3\mathrm{.}33& -5\mathrm{.}12& 4\mathrm{.}89\end{array}\right]$

a$)$ What is the variance of the $1^{st}$ input feature?

b$)$ What is the covariance between the $1^{st}$ and $2^{nd}$ features?

If the eigenvalues for $4$ features are:

$4\mathrm{.}22,0\mathrm{.}24,0\mathrm{.}08,0\mathrm{.}02$

What is the number of transformed features $(k)$ required for PoV$>97\%?$

Note: The problems are using Python syntax to represent arrays.