A First Course in Linear Algebra · Problem SLT-T15

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · range-linear-transformations

Problem

Suppose that

T: U \to V

and

S: V \to W

are linear transformations. Prove the following relationship between ranges.

\mathcal{R}(S \circ T) \subseteq \mathcal{R}(S)