Proving A0=0 for a Scalar and Zero Vector

Click For Summary

Homework Help Overview

The discussion revolves around proving that A0 equals the zero vector, where A is a scalar and 0 represents the zero vector. The participants explore the properties of scalar and vector multiplication in the context of vector spaces.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the form A0 + A0 = A0 + 0 and question how to manipulate this expression. There is a suggestion to consider the definition of vector addition and whether A0 + 0 can be equated to 0.

Discussion Status

The discussion is active, with participants providing hints and exploring different interpretations of vector addition. There is no explicit consensus, but some guidance has been offered regarding the properties of vector spaces.

Contextual Notes

There is a mention of the need to adhere to the basic laws of vector spaces, indicating that certain assumptions about vector addition may need to be clarified or checked.

cragar
Messages
2,546
Reaction score
3

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.
 
Physics news on Phys.org
cragar said:
can we say A0 + 0 = 0

Hi cragar! :smile:

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 :wink:
 
so then A(0+0)=0
 
Last edited:
cragar said:
is x a vector

uhh? :redface:

get on with it! :smile:
 
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
 
Last edited:

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 17 ·
Replies
17
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
18K
  • · Replies 5 ·
Replies
5
Views
1K
  • · Replies 3 ·
Replies
3
Views
3K