Proving Vector Addition and Associativity in D-3: Linear Algebra Homework

[sciencegirl1]

Homework Statement

F and G and H are vectors in D-3
a and b are real numbers

Proof that F+G=G+F

Proof that (F+G)+H=F+(G+H)

Homework Equations

The Attempt at a Solution

I did put F=a,b,c and G=a1,b1,c1 and H=a2,b2,c2 and put that in.
I just don´t know if that´s enough.

anyone who knows?

 

[quantumdude]

That sounds fine, as long as you explicitly show the manipulations. But yes, you should be allowed to use the fact that the real numbers are commutative and associative under addition.

 

[sciencegirl1]

thanks
how would you write it down in steps?

 

[matt grime]

What is D-3? And why did you mention then a and b are real numbers - you didn't use a or b.

 

[quantumdude]

matt has a point, this is a little sloppy.

F and G and H are vectors in D-3

I think you mean \mathbb{R}^3, no?

a and b are real numbers

Better still: a_i,b_i\in\mathbb{R} for i=1,2,3.

Then let F=<a_1,b_1,c_1>, G=<a_2,b_2,c_2>, and H=<a_3,b_3,c_3>.

how would you write it down in steps?

Add the vectors componentwise and use the familiar properties of the reals.

 

[matt grime]

I was confused by the question, and if I'm confused then that means you (the OP) might well be confused. The way to start with all questions is by making sure that you understand them clearly - writing it out so that someone else understands it is one way of doing that.

I don't know what D-3 means, and you introduce a and b in the question but they don't form any part of the question, for example. Are those a and b the same as the a and b (and then c, a1 a2 etc) that follow?

 

[HallsofIvy]

I might guess that D-3 means simply an abstract 3 dimensional vector space. But in that case, of course, commutativity and associativity of addition are part of the defining properties of a vector space so there is nothing to prove.

 

[Mark44]

My guess is that by D-3, she meant 3D, meaning three-dimensional (real) space.