Type solutions to the homework problems listed below using preferably LyX/ETEX word processors, see the class webpage for more information about their installation and tutorials. 1. (10 points) Use the STL class vector to write a C++ function that takes two vectors, a and b, of the same size and returns a vector c such that c[i] = a[i]b[i]. How many scalar multiplications are used to create elements of the vector c of size n? Provide a formula on the number of scalar multiplications in terms of n. What is the classification of this algorithm in terms of the Big-O notation