Please use Wolfram Mathematica coding to solve question below:

= - P4) (L 2.2.6) Build a 500 x 500 matrix A [aij] with diagonal entries Qji = 1, superdiagonal entries Ai,i-1 -0.5, and subdiagonal entries Qi+1, -0.5. (Hint: Construct these matrices using the Mathematica built-in Sparse Array.) a) Execute Linear Solve 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. = - P4) (L 2.2.6) Build a 500 x 500 matrix A [aij] with diagonal entries Qji = 1, superdiagonal entries Ai,i-1 -0.5, and subdiagonal entries Qi+1, -0.5. (Hint: Construct these matrices using the Mathematica built-in Sparse Array.) a) Execute Linear Solve 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