Indexing

1. task1 You are given a square matrix of an even size. (you are not supposed to test that the matrix is actually even and square, just use it). Imagine we split a matrix vertically and horizontally through the center. Return the matrix at the left-top.
2. task2 You are given a matrix with an even number of rows. Return a new matrix where the top half is exchanged with the bottom half of the initial matrix.
3. task3 You are given a vector with integer numbers. Return a vector that contains only that numbers of the initial vector, that are divisible by 3. Use the mod function to test divisibilty.

4. Create two functions filter_multiples and seive. The first one is filter_multiples(a, k), it removes all numbers from the vector a that are divisible by k and are strictly greater than k. For example, filter_multiples([1 5 10], 5) yields [1 5]

   The second one is sieve() and it is as follows:

        function a = sieve(n)
          a = 1:n;
          i = 2;
          while i < length(a)
            a = filter_multiples(a, a(i));
            i++;
          endwhile
        endfunction
   

   Explain in comments, what does sieve(n) do and how.

5. task5 You are given a matrix with two columns. Each row describes a person: his or her height and a type. There are two types of people: 1 and 2. Return three column-matrices of size 2.
   The first one contains a sum of heights for each type of people. The second one contains a mean height for each type. The third one contains a mean height excluding those who a higher than 2 meters or lower than 1 meter.
6. task6 Double all odd elements of a given row-matrix. For example, [1, 2, 3] -> [2, 2, 6].
   • does your solution work for two dimentional matrices?