Determinant exercise: show that

1. May 31, 2012

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/

2. May 31, 2012

Ray Vickson

RGV

3. May 31, 2012

sharks

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

4. May 31, 2012

dimension10

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.

5. May 31, 2012

Alistair Over

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

Attached Files:

• Dúvida fórum de álgebra.png
File size:
5.5 KB
Views:
49
6. May 31, 2012

HallsofIvy

Staff Emeritus
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.

7. May 31, 2012

dimension10

It does for me.