As fast as possible please! Solve beginning from " Find a general equation for R(T) " Consider the linear transformations T : R? –→ R° andS: R → R³ defined by the following formulasI – 2yT-2x + 4ySx – y- 2yx + y +2zFind the null space N(T) of T and the null space N(S) of S.Find the range R (T) of the above transformation T andthe range R(S) of the above transformation S.Find a general equation for R (T) as a subspace of IR.Use the rank-nullity theorem to find the dimensions ofthe range and the null space of the composed linear transformation ST.

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beginning from " Find a general equation for R(T

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...

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Question

As fast as possible please! Solve beginning from " Find a general equation for R(T) "

Consider the linear transformations T : R? –→ R° and
S: R → R³ defined by the following formulas
I – 2y
T
-2x + 4y
S
x – y
- 2y
x + y +2z
Find the null space N(T) of T and the null space N(S) of S.
Find the range R (T) of the above transformation T and
the range R(S) of the above transformation S.
Find a general equation for R (T) as a subspace of IR.
Use the rank-nullity theorem to find the dimensions of
the range and the null space of the composed linear transformation ST.

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