Be S = {v1 = (1,2, 1), v2 = (2,9,0), v3 = (3, 3, 4)} a subset of R and T : R³ → R? T(v1) = (1,0), T(v2) = (–1, 1), T(v3) = (0, 1). a) Find Ker (T) and a basis for Ker(T). What is the dim(Ket (T))? satisfies the theorem of b)dimension? T is iniecting? T IIs it Subiective? Is T isomorphism? iustify

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Be S = {v1 = (1, 2, 1), v2 = (2,9, 0), v3 = (3, 3,4)} a subset of R and T:
R → R?
T(v1) = (1,0), T(v2) = (-1, 1), T(v3) = (0, 1).
a)Find Ker(T) and a basis for Ker(T). What is the dim (Ket (T))? satisfies the theorem of
b)dimension? T is iniecting? T Is it Subiective? Is T isomorphism? justify
Transcribed Image Text:Be S = {v1 = (1, 2, 1), v2 = (2,9, 0), v3 = (3, 3,4)} a subset of R and T: R → R? T(v1) = (1,0), T(v2) = (-1, 1), T(v3) = (0, 1). a)Find Ker(T) and a basis for Ker(T). What is the dim (Ket (T))? satisfies the theorem of b)dimension? T is iniecting? T Is it Subiective? Is T isomorphism? justify
Expert Solution
Step 1

Given that  S=v1=1, 2, 1, v2=2, 9, 0, v3=3, 3, 4 be a subset of 3 and

    T : 32 

    Tv1=(1, 0), T(v2)=(-1,1), T(v3)=(0,1)

 

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