Determinant exercise: show that

[Alistair Over]

Hey people, could someone solve this problem and explain step by step? It's from a past exame and I really need to know how to do it, tried everything I know (not much tho). Please don't omit steps.Really appreciated!
imageshack.us/photo/my-images/403/dvidafrumdelgebra.png/

 

[Ray Vickson]

Hey people, could someone solve this problem and explain step by step? It's from a past exame and I really need to know how to do it, tried everything I know (not much tho). Please don't omit steps.Really appreciated!
imageshack.us/photo/my-images/403/dvidafrumdelgebra.png/

Your link does not load. Generally, though, what you are asking here violates the PF rules. You are supposed to show us your work first, then ask for help.

RGV

 

[DryRun]

Just attach the picture directly to your own post. No need to use external image hosting sites.

 

[dimension10]

Hey people, could someone solve this problem and explain step by step? It's from a past exame and I really need to know how to do it, tried everything I know (not much tho). Please don't omit steps.Really appreciated!
imageshack.us/photo/my-images/403/dvidafrumdelgebra.png/

I think you can try finding an expression for each element of $A_n$ first. Let us call it $x_{ijn}$

$$ x_{ijn}=(a-b)\delta_{ij}+b $$
$$ x_{ijn}=a\delta_{ij}+(1-\delta_{ij})b $$

Then you can somehow show the result. Not sure how you can continue though.

 

[Alistair Over]

here is the atachment! Sorry but I have my examination tomorrow, I'm desesperate :s

 

[HallsofIvy]

Proof by induction- if you expand each determinant, $A_{n+1}$, by the first row, you get a times $A_n$+ n-1 times b times a subdeterminant.

 

[dimension10]

Your link does not load.

It does for me.