Final answer:
A linear transformation from R³ to R² is a function that maps three-dimensional vectors to two-dimensional vectors.
Step-by-step explanation:
The correct answer is 1) A transformation that maps a three-dimensional vector to a two-dimensional vector. A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. When we refer to a transformation from R³ (three-dimensional real number space) to R² (two-dimensional real number space), we are describing a function that takes a vector with three components and returns a vector with two components.
For example, a matrix A that is 2x3 can represent such a transformation. If v is a vector in R³, the product Av will be a vector in R². This is achieved by multiplying each element of the vector in R³ by the corresponding elements in matrix A and summing up the results to produce the entries of the vector in R².