Consider solving the matrix system Ax = b by first factoring A (aij) into LU and then solving Ly = b and Ux y, where A is a n n nonsingular matrix. L = (lij) is an unit lower triangular matrix and U = (uij) is an upper triangular matrix. Show that the LU factorization algorithm described below requires 3 - multiplications & divisions and additions & subtractions input n, (aij) for k 1 to n do for j- k to n do k-1 end do for i k + 1 to n do k-1 lik is Ush 8 ik Ukk end do end do output (lij), (Uij