Final answer:
A linear transformation is a function between vector spaces that preserves vector addition and scalar multiplication. It can be represented by matrix multiplication and satisfies the linearity properties.
Step-by-step explanation:
What makes something a linear transformation?
A linear transformation is a function between vector spaces that preserves vector addition and scalar multiplication. In other words, it satisfies the linearity properties. A linear transformation can be represented by matrix multiplication when the vector spaces are finite-dimensional. Therefore, the answer is A. Matrix Multiplication and B. Linearity Properties.
For example, consider the transformation T: R^2 -> R^2 defined by T(x, y) = (3x - 2y, 2x + y). This transformation preserves vector addition and scalar multiplication, making it a linear transformation.