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Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft})
Chapter 2, Problem 33(choose chapter or problem)
QUESTION:
Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft}).
Questions & Answers
QUESTION:
Prove Theorem 2.2 for the case that ft is infinite, that is, R(T) = spm({T(v):vft}).
ANSWER:Step 1 of 2
Suppose V and W be vector spaces and be linear.
Let be a basis for V which is not finite.
To prove that .
Since is a basis for V, for each .
Again, being a subspace contains .
Thus,