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• read,
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with the Computer Science Department's Statement on Academic Integrity before turning in your assignment.

1. Write a method called scalarProduct that computes the scalar product of two mathematical vectors (represented as lists). The scalar product is:

   a₀b₀ + a₁b₁ + ... + a_n-1b_n-1

2. Write a method that computes the alternating sum of all elements in a list of numbers. For example, if alternatingSum is called with a list containing

   1   4   9   16   9   7   4   9   11

   Then it computes

   1 - 4 + 9 - 16 + 9 - 7 + 4 - 9 + 11

   which is, of course, -2.

3. Write a method reverse that reverses the sequence of elements in an array. For example, if reverse is called with an array (or list) containing

   1   4   9   16   9   7   4   9   11

   then the array is changed to

   11   9   4   7   9   16   9   4   1

4. Write a predicate method equals that checks whether two arrays have the same elements in the same order.

5. Write a predicate method sameSet that checks whether two arrays have the same elements in some order, ignoring multiplicities. For example, the two arrays

   1   4   9   16   9   7   4   9   11

   and

   11   11   7   9   16   4   1

   would be considered to have the same set. You may or may not need one or more helper methods.

6. Write a predicate method sameElements that checks whether two arrays have the same elements in some order, with the same multiplicities. For example,

   1   4   9   16   9   7   4   9   11

   and

   11   1   4   9   16   9   7   4   9

   would be considered to have the same elements, but

   1   4   9   16   9   7   4   9   11

   and

   11   11   7   9   16   4   1

   would not.

   You may or may not need one (or more) helper method(s).