Final answer:
The correct answer is option A. The vector b is a linear combination of the columns of matrix a. The exponential distribution best describes a scenario where fewer individuals can achieve a task as the difficulty increases, and a uniform dispersal pattern is characterized by even spacing between individuals in a population.
Step-by-step explanation:
The vector b is a linear combination of the columns of matrix a. This pertains to the field of linear algebra within mathematics, where vectors are often represented as combinations of other vectors, typically the columns of a matrix. When discussing the multiplication of a vector by a scalar, as shown in one of the provided references, a new vector is formed that is parallel to the original vector, which is an example of linear scaling.
In the context of probability distributions, the scenario where many people can run a short distance but fewer can run longer distances suggests a distribution where the frequency rapidly decreases as the value increases; the exponential distribution is characterized by this behavior. When defining a variable, the correct description is that it is something whose value can change; variables are a fundamental concept in mathematics and statistics as they allow for the representation and analysis of quantities that can vary.
Looking at dispersal patterns in populations, a uniform dispersal pattern is characterized by even spacing between individuals, which is different from a random pattern where the spacing is not predictable.