Which property is NOT true for linear transformations?

Linear transformations have specific properties that adhere to linearity, meaning they fulfill two primary conditions: they must be additive and homogeneous. One of the defining characteristics of a linear transformation is that it maintains the structure of the vector space.

The option regarding the creation of non-linear outputs does not align with the definition of linear transformations. Since linear transformations operate under the framework of linearity, they map vectors from one space to another while maintaining the linear relationships. This means that if you take a linear combination of inputs, the output will also be a linear combination of the corresponding outputs. Therefore, any output from a linear transformation will consistently maintain linearity; it cannot yield non-linear outputs.

In contrast, the properties of scalability, preservation of the origin, and mapping lines to lines are all fundamental characteristics of linear transformations. They scale input vectors appropriately, send the zero vector to the zero vector (thus preserving the origin), and maintain the linear nature of lines during transformation, ensuring that linear phenomena are preserved throughout the mapping process.