Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5

Operations on vectors

In mathematics, an n-dimensional vector is a list of numbers of length n. For example, [2,5,12] is a 3-dimensional vector, and [45,27,3,-4,6] is a 5-dimensional vector. One of the basic operations on vectors is scalar multiplication. In this operation, every element of a vector is multiplied by some number. For example, if we scalar multiply the 3-dimensional vector [2,7,4] by 3 the result is the 3-dimensional vector [6,21,12]. Write a 3-place predicate scalarMult whose first argument is an integer, whose second argument is a list of integers, and whose third argument is the result of scalar multiplying the second argument by the first. For example, the query scalarMult(3,[2,7,4],Result) should yield Result = [6,21,12].

Another fundamental operation on vectors is the dot product. This operation combines two vectors of the same dimension and yields a number as a result. The operation is carried out as follows: the corresponding elements of the two vectors are multiplied, and the results added. For example, the dot product of [2,5,6] and [3,4,1] is 6+20+6, that is, 32. Write a 3-place predicate dot whose first argument is a list of integers, whose second argument is a list of integers of the same length as the first, and whose third argument is the dot product of the first argument with the second. For example, the query dot([2,5,6],[3,4,1],Result) should yield Result = 32.

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