Complex sentence: A second example of the difference between codomain and image is demonstrated by the linear transformations between two vector spaces--in particular, all the linear transformations from R 2 to itself, which can be represented by the 2x2 matrices with real coefficients.
Split into simpler sentences: A second example of the difference between codomain and image can be seen by considering the linear transformations between two vector spaces. In particular, consider all the linear transformations from R 2 to itself, which can be represented by the 2x2 matrices with real coefficients.