Final answer:
The scalar r that makes ax = rx is directly equal to the scalar constant a, since scalar multiplication of vectors is commutative.
Step-by-step explanation:
To determine a scalar r such that ax = rx, we are tasked with finding the scalar multiple that makes the vectors equivalent. This involves understanding scalar multiplication of vectors and isolating the scalar r.
For any vector x and scalar a, if ax is equal to rx, then by definition, r must be equal to a because each component of vector x is multiplied by the scalar to get the resultant vector ax (or in this case, rx).
Therefore, the value of scalar r is directly equal to the given scalar constant a.