Using a matlab script file create a vector of 100 equidistant points on the interval

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1. The Chebyshev polynomials of the first kind can be derived from the recurrence relation 0( ) = 1, 1( ) = , +1( ) = 2 ( ) − −1( ) where = 1,2, … , . Create a MATLAB file to create and plot the above equations.

(a) Using a MATLAB script file, create a vector of 100 equidistant points on the interval [−1,1]. (1 mark)

(b) Let = 8, initialize a matrix of size 30-by-10 whose all elements are zero. The column refers to the ( ), while row refers to the corresponding components. (1 mark)

(c) Use nested for loop to evaluate all the polynomials at each point of and store the results in matrix . (4 marks)

(d) Use command subplot to plot the first 5 Chebyshev polynomials in the same figure panel and plot the last 5 polynomials in another panel below the first panel, as illustrated in an example below. Label the axes and include the appropriate legends.

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