Please show all work and explanations for the double function.

Write a MATLAB function half that removes every other element from a vector of arbitrary length, creating a shorter vector made out of only the odd-numbered elements of the original vector; and a MATLAB function double that creates a longer vector by adding an additional element between neighboring elements in the original vector. Each new element should equal the average of its neighboring elements. Use only matrix/vector manipulations: do NOT use loops. Test your solution by applying half and double to the vectorx [12345654 3 21]. What happens after the execution of half followed by double, and double followed by half