- #1

SeannyBoi71

- 84

- 0

## Homework Statement

Let

*U*be a subspace of ℝ

^{n}. Show that if

**u**[itex]\in[/itex]

*U*[itex]\bigcap[/itex]

*U*

^{[itex]\bot[/itex]}, then

**u**=

**0**.

## Homework Equations

## The Attempt at a Solution

I know that U

^{[itex]\bot[/itex]}will be orthogonal to U, so any vector

**u**in U dotted with any vector in U

^{[itex]\bot[/itex]}will equal 0. But that does not necessarily mean that

**u**=

**0**so I must prove something else. I don't know where to include the intersect into all of this, we have never used that kind of thing before.