- 86

- 0

**1. 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

**3. 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?

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**