Final answer:
The smallest possible dimension of the column space of a matrix, col(A), is zero, which occurs when all column vectors of the matrix are the zero vector, indicating no linearly independent vectors.
Step-by-step explanation:
The question 'What is the smallest possible dimension of col(a)?' pertains to the concept of matrix column spaces in linear algebra.
The column space of a matrix, denoted as col(A), is defined as the set of all possible linear combinations of its column vectors. The dimension of the column space, also known as the rank of the matrix, is the maximum number of linearly independent column vectors in the matrix.
The smallest possible dimension of col(A) is zero. This occurs when all the column vectors of matrix A are the zero vector. In this case, there would be no vectors in the column space other than the zero vector itself, which means that there are no linearly independent vectors and thus the dimension, or rank, is zero.