Q5. Let T: R → Rm be a linear transformation. Suppose that there exists a map S: Rm → Rª with the property that that S(7)=7T(V) for alle Rm and 7ER". (a) Prove that S is a linear transformation. (b) Since both T and S are linear, we can find matrices A and B such that T = T₁ and S=TB. Prove that B = AT.
Q5. Let T: R → Rm be a linear transformation. Suppose that there exists a map S: Rm → Rª with the property that that S(7)=7T(V) for alle Rm and 7ER". (a) Prove that S is a linear transformation. (b) Since both T and S are linear, we can find matrices A and B such that T = T₁ and S=TB. Prove that B = AT.
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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Transcribed Image Text:Q5. Let T: R → Rm be a linear transformation. Suppose that there exists a map S: Rm → R
with the property that that
S() = T(V)
for alle Rm and ER".
(a) Prove that S is a linear transformation.
(b) Since both T and S are linear, we can find matrices A and B such that T = T₁ and
S=TB. Prove that B = AT.
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