Given an iterative algorithm below which defines the $k+1$ elements of vectors A and $B$ :

$A(k+1)=10-B(k)$

$B(k+1)=B(k)+\frac{A(k)}{500}$

$A(1)=10,B(1)=0$

a$.$ Find the value of A and $B$ on the $3^{rd}$ iteration.

b$.$ Find the value of A and $B$ on the ${1000}^{th}$ iteration.

c$.$ What are the steady state values of A and $B($i$.$e$.,A(k),B(k),k?$

d$.$ Create good plots of A and B as a function of iteration number.