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## Homework Statement

If x = (x1, x2) and y = (y1, y2)....

Show that <x,y> = 3(x1)(y1) - (x1)(y2) - (x2)(y1) + 3(x2)(y2)

## Homework Equations

I know that to define it as an inner product space, the following must be correct:

<x,y> = <y,x>

a<x,y> = <ax,y>

<x,y+z> = <x,y> + <x,z>

<x,x> >/= 0

<x,x> = 0 therefore x=0

## The Attempt at a Solution

I have a fair idea what the rules above mean, however I have no clue how to apply it to the question. Help??