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).
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
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 4EQ
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please send step by step handwritten solution Q3 part a
![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14815be2-6dae-4474-bc6b-06046c1707f6%2Fe0043068-0a58-48ad-84b2-fbde69c4bcfe%2Ftiyye6_processed.png&w=3840&q=75)
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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