(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra, Linear Maps

**Physics Forums | Science Articles, Homework Help, Discussion**