# Linear algebra proofs

1. Mar 14, 2009

### sciencegirl1

1. The problem statement, all variables and given/known data

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)

2. Relevant equations
3. 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?

2. Mar 14, 2009

### Tom Mattson

Staff Emeritus
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.

3. Mar 14, 2009

### sciencegirl1

thanks
how would you write it down in steps?

4. Mar 14, 2009

### 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.

5. Mar 14, 2009

### Tom Mattson

Staff Emeritus
matt has a point, this is a little sloppy.

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

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 $H=<a_3,b_3,c_3>$.

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

6. Mar 14, 2009

### 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?

7. Mar 14, 2009

### HallsofIvy

Staff Emeritus
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.

8. Mar 14, 2009

### Staff: Mentor

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

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