Using Mathematica, please create the correct code to answer all parts to this question:

P4) (L 2.2.6) Build a 500 x 500 matrix A = ajj with diagonal entries ani = 1, superdiagonal entries ai,i-1 = -0.5, and subdiagonal entries di+1,i = -0.5. (Hint: Construct these matrices using the Mathematica built-in Sparse Array.) a) Execute LinearSolve for the linear system Ax = b where bi = 1 for every i. Use the command LU Decomposition to determine the condition number of A. b) Repeat exercise a) for a 100 x 100, 200 x 200, 300 x 300, 400 x 400 matrix having the same diagonal, subdiagonal, superdiagonal. Plot the condition number as a function of the matrix size. The command List Plot will help here