This was part of the online test on Moodle and you should go there to see the solutions.
The solutions there include the Hilbert matrix even though that was not part of the test.
The instructions asked you to comment on Wikipedia's definition of the Hilbert matrix.
Our definition has $1/(i+j+1)$ in position $(i,j)$, whereas Wikipedia has $1/(i+j-1)$.
The difference just that Wikipedia numbers the rows and columns from $1$ to $n$, whereas
we number them from $0$ to $n-1$. For us, the top left corner has $i=j=0$ so the
entry is $1/(0+0+1)=1$. For Wikipedia, the top left corner has $i=j=1$ so the
entry is $1/(1+1-1)=1$, which is the same.
Task 2: Onion matrices
This was part of the online test on Moodle and you should go there to see the solutions
(which give several alternative approaches).
Task 3: Moving average
This was part of the online test on Moodle and you should go there to see the solutions.
The solutions define a function a_basic(n, k) which is easy to understand but
not super-efficient, and another function a(n, k) which is better but
less obvious.