4. (10 points) A matrix A E Rn n is tridiagonal if aij = 0 whenever li-jl > i. For example, 1 2 0 0 12 30 A- 0033 is a 4 4 tridiagonal matrix. Write pseudocode for an algorithm that computes the product y Aa for any tridiagonal A E R"n and a e R" that uses a minimal number of arithmetic operations. How many arithmetic operations does your algorithm need to compute y? Hint: your solution should be similar to the algorithm for matrix-vector multiplication but not identical to that algorithm. In particular, your method should be significantly more efficient because it exploits the tridiagonal structure of A. It is fine to report the operation count using Big Oh notation, e.g., you can use O(n2) instead of 2n2 to state the operation count for standard matrix-vector multiplication