Answer it by using Python.

$9\mathrm{.}6$ Recursive averaging. Suppose that $u_1,u_2,$dots is a sequence of $n-$vectors. Let $x_1=0,$ and

for $t=2,3,$dots, let $x_t$ be the average of $u_1,$dots,$u_{t-1},$ i$.$e$.,x_t=\frac{u_1+\text{c}\text{d}\text{o}\text{t}\text{s}+u_{t-1}}{t-1}.$

Express this as a linear dynamical system with input, i$.$e$.,x_{t+1}=A_t{x}_t+B_t{u}_t,t=1,2,$dots

$($with initial state $x_1=0).$ Remark. This can be used to compute the average of an

extremely large collection of vectors, by accessing them one$-$by$-$one.