Final answer:
The question revolves around the concept of linear independence in linear algebra, where vectors in ℝ⁽ are considered linearly independent if none of them can be expressed as a linear combination of the others. A matrix can transform these vectors while preserving their independence, suggesting the matrix has full rank.
Step-by-step explanation:
The question seems to be a bit fragmented and unclear, but it revolves around linear algebra concepts, particularly the relationship between matrices and linear independence of vectors in ℝ⁽. If a set of vectors in ℝ⁽ is linearly independent, each vector in the set cannot be expressed as a linear combination of the others.
This means that for a matrix A of size m × n, if it transforms a set of linearly independent vectors in ℝ⁽ and the set remains linearly independent after the transformation, this implies that A has full rank (assuming A's rank is less than or equal to m and n). However, without more context regarding the specifics of the matrix A and its actions on the vectors in question, providing a definitive answer to whether a given statement is true is challenging.