Part A$.5$ marks

We wish to compute a row vector of n $=1000000$ entries, where entry I of the vector equals $1/$n sin $($ipi$/$n$).$ We apply the following approaches:

A$1$: The vector u is created using a for$-$loop without pre$-$initializing the array.

A$2$: The vector v is created using a for$-$loop and it is first pre$-$initialized using Matlab$$s zeros command.

A$3$: The vector w is created without using a loop.

Use Matlab$$s tic and toc to measure the time required for each approach. $($Include the pre$-$initialization for vector v$.)$ Determine which method is the most efficient and which method is least efficient. Is there a significant difference in the compute time?