# Homework Help: 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:
107
6. May 31, 2012

### 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.

7. May 31, 2012

### dimension10

It does for me.