Final answer:
The statement that a line in R² is a one-dimensional subspace is false, because not all lines pass through the origin, which is a requirement for being a subspace.
Step-by-step explanation:
The statement that a line in R² is a one-dimensional subspace is false. A subspace in R² must satisfy certain criteria, such as containing the zero vector, being closed under vector addition and scalar multiplication. While a line that passes through the origin does satisfy these conditions and is indeed a subspace, not all lines do this. A general line in R², which does not go through the origin, doesn't include the zero vector, hence it is not a subspace.
For example, the line y = 2x + 1 does not go through the origin and therefore is not a one-dimensional subspace of R². Only if the line has an equation of the form ax + by = 0, which implies it passes through the origin, it can be considered a subspace of R².