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Consider the following linear maps T : R2 –→ Rª and S : Rª → M(2,R) defined as follows: 2x + 3y %3D -y I + y 3r r + y S( %3D 2z 3w w a) Determine if the composition S o T is injective (one-to-one). b) Determine if S is an isomorphism. If yes, compute the inverse map (you must write down a formula for the inverse linear map if it exists)

Consider the following linear maps T : R2 –→ Rª and S : Rª → M(2,R) defined as follows: 2x + 3y %3D -y I + y 3r r + y S( %3D 2z 3w w a) Determine if the composition S o T is injective (one-to-one). b) Determine if S is an isomorphism. If yes, compute the inverse map (you must write down a formula for the inverse linear map if it exists)

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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3. Consider the following linear maps T: R2 –→ Rª and S : Rª → M(2, R) defined as follows: 2x + 3y T( -y 3x r+y - 2z S( %3D w a) Determine if the composition SoT is injective (one-to-one). b) Determine if S is an isomorphism. If yes, compute the inverse map (you must write down a formula for the inverse linear map if it exists)
Transcribed Image Text:3. Consider the following linear maps T: R2 –→ Rª and S : Rª → M(2, R) defined as follows: 2x + 3y T( -y 3x r+y - 2z S( %3D w a) Determine if the composition SoT is injective (one-to-one). b) Determine if S is an isomorphism. If yes, compute the inverse map (you must write down a formula for the inverse linear map if it exists)
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