The figure below shows where a linear transformation maps the three standard basis vectors from its domain.
The grids in the figures are unit grids.
Vectors with their tip on the grid are in the -plane, while vectors with their tip not on integer-coordinate points the grid are
not in the -plane.

for and .

The set of vectors is (select all that apply):
A. a basis for the codomain B. a basis for the domain C. a spanning set D. linearly independent

The set of vectors is (select all that apply):
A. a spanning set B. a basis for the codomain C. linearly independent D. a basis for the domain

The linear transformation is (select all that apply):
A. an injection (i.e., one-to-one) B. a surjection (i.e., onto) C. a bijection (i.e., isomorphism)

Find the matrix for the linear transformation (relative to the standard
basis in the domain and codomain). That is, find the matrix such that . For instance, enter [ [1,2], [3,4] ] for the matrix .

In order to get credit for this problem all answers must be correct.