- 2.1

Recall a linear transformation is a map

*T*such that*T*(*x*+*y*) =*T*(*x*) +*T*(*y*) and*T*(*c**x*) =*c**T*(*x*).- We can also apply this to a general linear combination.
- Differentiate and integration are examples.
- Reflections, projections (there are multiple versions)
- Translation is not an example.
- Identity and zero transformations

null space and kernel, range and image

Theorem: these are subspaces

image of subspaces T(W)

prove rank-nullity. Pick a basis for null space and extend.

One-to-one