B$1$ Write a function powersarray $($b$)$ that takes a list $($or $1-$dimensional numpy array$)$ of length $d$ representing a row vector $b_0,$dots,$b_{d-1}($for some $d)$ and returns a numpy array representing the matrix $([b_0^0,$dots,$b_{d-1}^0],[vdots,$vdots$],[b_0^{d-1},$dots,$b_{d-1}^{d-1}]).$

B$2$ Write a function ApproxSolver$1($a$0,$ a$1,$ b$0,$ b$1,$ m$)$ that takes as input two entries $a0,$ a$1$ representing the second order difference equation $a_0{x}_n+a_1{x}_{n+1}+x_{n+2}=0,$ and two more b$0,$ b$1$ representing initial conditions $(x_0,x_1)=(b_0,b_1),$ along with a value $m,$ and outputs an integer which is an approximate value of $x_m$ by $($assuming distinct roots of the auxiliary equation$).$

B$3$ Adjust your function to ApproxSolver$2($a$,$ b$,$ m$),$ which is as above, but accepts as inputs lists $a,b$ of length len$(a)=$len$(b)=d$ for any positive integer $d,$ representing the degree of the equation $($again assuming all distinct roots$).$