# Vectors problem

1. Mar 28, 2005

### kidia

This one:
a)Let V be a vector space and let x be a vector in V.
i)Show that b0=0 for each scalar b.
ii)Show that if bx=0, then either b=0 or x=0

2. Mar 28, 2005

### whozum

Im assuming you mean the magnitude.
The zero vector has components <0,0,0>, the magnitude of this vector is $$\sqrt{0^2+0^2+0^2} = 0.$$

b<x,y,z> = <bx,by,bz>

b<0,0,0> = <b0,b0,b0> = 0

ii) follows from i)

3. Mar 28, 2005

### HallsofIvy

Staff Emeritus
No, there is no reason to assume that kidia "means the magnitude" (and you don't then use "magnitude"). More importantly,there is no reason to assume that kidia meant R3 or any Rn. These theorems are true in any vector space.

kidia, what happens if you multiply a(x+ 0)? What does that tell you about a0?

Similarly, what happens if you multiply (a+ 0)x?