# ICE: Matlab Flow

Recall that the three-term recurrence relation
for Chebyshev polynomials is given by
\[
T_{k+1}(x) = 2xT_k(x)-T_{k-1}(x),
\]
where we know that \(T_0(x) = 1,\) and \(T_1(x)=x,\)
for \(x\in[-1,1].\)
Given some maximal degree \(K\) that we choose, write a script that
uses this relation to generate a \((K+1)\times N\) array
`T`
whose \(k^\text{th}\) row comprises the values of \(T_{k-1}\)
at some vector \(x\) of length \(N\), which you provide.
In other words, `T(k+1,n)`\(=T_k(x_n)\)
for \(k=0,1,\dots,K\) and \(n=1,2,\dots,N\).
Your script should then plot the rows of
`T`.

A solution for the
final is available.