# 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`.

The "final exam" for this course will take place
at 8:00 AM on Tuesday, 12 December. This will be an ordinary
50 minute test. It will be comprehensive, but weighted toward
the latter half of the semester. As always, paper notes will
be permitted, but no electronic devices will be allowed.

A
Solution example is available
for the quiz.

Assignment A is posted.