# Thread: Matrix proof - a question

1. ## Matrix proof - a question

Can anyone tell me why the summation's upper bounds 4 and 3 are used in the attached proof? Thanks. I'm new to the forum, can't seem to get the equations to come out correctly, so I took a screen shot of them instead.

2. ## Re: Matrix proof - a question

Originally Posted by aerzo
Can anyone tell me why the summation's upper bounds 4 and 3 are used in the proof below? Thanks.

Let A = [aij], B = [bij], C = [cij], AB = D = [dij], BC = E = [eij], (AB)C = F = [fij], and A(BC) = G = [gij]. To show that fij = gij for all i, j:

[tex]
4 4 3
fij = Σ dikckj = Σ (Σ airbrk) ckj
k=1 k=1 r=1
and
3 3 4
gij = Σ airerj = Σ airbrkckj)
r=1 r=1 k=1

3. ## Re: Matrix proof - a question

Ok, I'm going to play with that, sorry for the confusing post.

4. ## Re: Matrix proof - a question

Originally Posted by aerzo
Ok, I'm going to play with that, sorry for the confusing post.
Somewhere in the instructions you must have been told the dimensions of those matrices.
It seems some are $\displaystyle 4\times 3$ while others are $\displaystyle 3\times 4$.

5. ## Re: Matrix proof - a question

Originally Posted by Plato
Somewhere in the instructions you must have been told the dimensions of those matrices.
It seems some are $\displaystyle 4\times 3$ while others are $\displaystyle 3\times 4$.
Thanks very much, sorry I didn't get around to fixing the text.