Write a function in Matlab that takes as input a size n and a tridiagonal matrix given as three vectors: n 1 vector v representing the main diagonal, (n 1) 1 vector w representing the upper diagonal, and (n 1) 1 vector z representing the lower diagonal. Have this function output the LU factorization with the U as two vectors and the L as one vector representing the diagonals. Also output the number of flops used. Use only basic programming.

(a) Write out or print out your function.

(b) Run the case with n = 10, v the vector of 2s, w and z the vector of 1s, and b the vector of 1s. Write down your results for the diagonals of L and U.

(c) Run the case with n = 50 and n = 100 with v the vector of 2s, w and z the vector of 1s. Write down your results for the number of flops used