T:V \to W is the linear transformation of the vector

Corbin Walton

Corbin Walton

Answered question

2022-02-23

T:VW is the linear transformation of the vector spaces V and W. Let's take v0 which is an element of V as T(v0)=ω0.
How can I show that all the solutions of the equation T(v)=ω0 are of the form of v=v0+u? u is an element of N(T).

Answer & Explanation

Cheryl Stark

Cheryl Stark

Beginner2022-02-24Added 7 answers

Let Tv=w, and suppose that s is a solution of Tx=w. Then
T(sv)=TsTv=ww=0
Therefore sv is in the nullspace of T. Hence sv=u, i.e. s=v+u, for some uN(T).
faraidz3i

faraidz3i

Beginner2022-02-25Added 10 answers

Thanks for your answer.

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