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linear combination

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If T: U â?' V is any linear transformation from U to V and B = {u 1, u 2, ..., u n} is a basis for U, then set T(B) = {T(u 1), T(u 2), ... T(u n)}

a. spans V
b. spans U
c. is a basis for V
d. is linearly independent
e. spans the range of T

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Solution Summary

A linear combination is clearly evaluated in this case.

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The correct answer is e. Spans the range of T.
Every element x from the range of T can be written in the form
x = T(y) for some y in U
But since y ...

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