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## Homework Statement

If we define V as the set of vectors in R^2 with vector addition defined as it normally is, but scalar multiplication defined to be k(a,b)=(k

^{2}a,k

^{2}b), then V is not a vector space. Find all axioms that fail (and explain why they fail).

## Homework Equations

Axioms:

1. If

**u**and

**v**are objects in V, then

**u**+

**v**is in V.

2.

**u**+

**v**=

**v**+

**u**

3.

**u**+(

**v**+

**w**)=(

**u**+

**v**)+

**w**

4. There is an object

**0**in V, called a

**zero vector**for V, such that

**0**+

**u**=

**u**+0=

**u**for all

**u**in V.

5. For each

**u**in V, there is an object -

**u**in V, called a

**negative**of

**u**, such that

**u**+(-

**u**)=(-

**u**)+

**u**=

**0**.

6. If

*k*is any scalar and

**u**is any object in V, then k

**u**is in V.

7.

*k*(

**u**+

**v**)=

*k*

**u**+

*k*

**v**

8. (

*k*+

*l*)

**u**=

*k*

**u**+

*l*

**u**

9.

*k*(

*l*

**u**)=(

*k*

*l*)

**u**

10. 1

**u**=

**u**

## The Attempt at a Solution

I couldn't figure out how to start.

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