Proving A0=0 for a Scalar and Zero Vector

[cragar]

Homework Statement

prove A0=0
where 0 is the zero vector
and A is a scalar

The Attempt at a Solution

so i know we need to get it in the form
A0 + A0 = A0+ 0
but I am not sure how to get there
can we say A0 + 0 = 0
any input will be appreciated.

 

[tiny-tim]

can we say A0 + 0 = 0

Hi cragar!

You can't say A0 + 0 = 0 because (although it's true), it's not one of the basic laws of vector spaces.

Hint: try the definition of vector addition, 0 + X = X

 

[cragar]

so then A(0+0)=0

 

[tiny-tim]

is x a vector

uhh?

get on with it! ​

 

[cragar]

so then A(0+0)=A0
A0+A0=A0
then we subtract A0 from both sides
then we get A0=A0-A0

thanks for your help