81.4k views
2 votes
What makes something a linear transformation?

Options:
A. Matrix Multiplication
B. Linearity Properties
C. Scalar Addition
D. Nonlinear Elements

User Amechi
by
8.1k points

1 Answer

3 votes

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.

User Alejandro Huerta
by
7.6k points