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## Homework Statement

Let

*V*=

**C**

^{n}and

**1**be all ones vector

**1**= e

_{1}+ ... +e

_{n}. Let

*W*be the subspace of

*V*spanned by those vectors of the form [tex]\lambda[/tex]e

_{1}+ [tex]\lambda[/tex]e

_{2}+ ... + [tex]\lambda[/tex]e

_{n}such that [tex]\lambda[/tex]

_{1}+ ... + [tex]\lambda[/tex]

_{n}= 0 [tex]\in[/tex]

**C**. Prove that there is a direct sum decomposition

*V*=(

**C***

**1**) [tex]\oplus[/tex]

*W*

as complex vector spaces.

## Homework Equations

*V*=(

**C***

**1**) [tex]\oplus[/tex]

*W*

How should I approach this problem?