Suppose u is a message and the corresponding encoded message is v. Note: You are answering these questions for a general u and v, not the specific ones you might have obtained in part 1 of the lab. 11. How many elements does the vector u have? How many elements does the vector v have? 12. Explain why the coded message we obtain v must be in the Nullspace of the matrix H. We have the following theorem. Theorem 1: If H is the matrix given in problem 5, and if x is in Nul(H) then x + ei is not in Nul(H). 13. Fill in the blanks of the proof below. Give a reason for each step. Proof: Since x is in Nul(H), Hx = . But Hei = = 0 . Thus H(x + ei) = = 0 + hi = hi = 0, and x + ei is not in Nul(H). This result means that if a