- #1
*melinda*
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Homework Statement
Suppose that T is a linear map from V to F, where F is either R or C. Prove that if u is an element of V and u is not an element of null(T), then
V = null(T) (direct sum) {au : a is in F}.
2. Relevant information
null(T) is a subspace of V
For all u in V, u is not in null(T)
For all n in V, n is in null(T)
T(n) = 0, T(u) not= 0
The Attempt at a Solution
I think I should let U = {au : a is in F} and show that it's a subspace of V. Then I can show that each element of V can be written uniquely as a sum of u + n. Should I do this by showing that (u, n) is a basis for V?