Will require use of MATLAB

A Vandermonde matrix is an n times n matrix formed from a vector w vector = (w_0, w_1, w_2, ..., w_n - 1) as follows: V (w vector) = (w^n - 1 _0 w^n - 1 _1 w^n - 1 _2 w^n - 1 _n - 1 w^n - 2 _0 w^n - 2 _1 w^n - 2 _2 w^n - 2 _n - 1 ... w^2 _0 w^2 _1 w^2 _2 w^2 _n - 1 w_0 w_1 w_2 w_n - 1 1 1 1 1). You may generate Vandermonde matrices using the MATLAB command vander, which takes the vector w vector as its single parameter. (a) Consider the Vandermonde matrix generated with w vector = [10.0: 0.1: 11.0]. Solve the system V (w vector) x vector = b vector where b vector = [1; 9; 1; 9; 1; 9; 1; 9; 1; 9; 1]^T using LU decomposition and Forward/Backward solver. Plug your answer back into the system and compute the result. What do you observe? Provide the result you computed. (You can use your code from Question 3, or MATLAB's built-in linear solver. You can check (not required) that PALU does in this case not lead to more accurate results than LU.) (b) Compute the condition number of the matrix V (w vector) and use this to explain the observed discrepancy. (You may calculate the condition number of a matrix A using the cond command. This command returns an explicit value of the condition number for the provided matrix.)