Consider the following linear maps T : R² → Rª and S : Rª – M(2,R) defined as follows: 2x + 3y T( %3D -y x + y 2z w a) Determine if the composition S oT is injective (one-to-one).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
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Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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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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