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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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:ℝp→ℝn and T:ℝn→ℝm be a linear transformations.

We have to prove the mapping x→→TSx→ is a linear transformation.

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