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.

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.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...

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Question

Let S : RP → R" and T : R" → Rm 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(x)) is a linear transformation.

Expert Solution

Step 1

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

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

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