Let S : RP→→R" and T : R" → R" be linear transformations. Prove the following statement. Your work should be legible, and all your logic should be clear and justified. The mapping → T(S()) is a linear transformation.

Given that $S:{\mathrm{ℝ}}^p\to {\mathrm{ℝ}}^n$ and $T:{\mathrm{ℝ}}^n\to {\mathrm{ℝ}}^m$ be a linear transformations.

We have to prove the mapping $\overrightarrow{x}\to T\left(S\left(\overrightarrow{x}\right)\right)$ is a linear transformation.