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What is An?

the matrix

commonly seen as Ax=b.
this is An=0.

Are you saying n is an eigenvector ?

honesly i dont know wat to do. this is what the teacher asked us

Or are you say An is the matrix?

idk..lol

Ok I think
|dw:1340595284758:dw|
and
|dw:1340595304816:dw|

Is that what you think?

But that doesn't make since that A_n would be the matrix with nothing but zero entries

do you mean the determinant is 0?

|A_n|=0?

that would make since

sense*

I think that is what you mean

so do you know how to find the determinant of a matrix?

ya ad-bc

Try finding the determinant of A_2 ?
What do you get?

zero

Ok what about A_3

same

Ok so we have convinced ourselves that |A_n|=0
But we must prove it

|dw:1340595692432:dw|

I would just show a little work for this
show a pattern you know

like how you did for A_3 and then do the nth term
you know what I mean?

how do u find determinant for 3x3 or bigger matrix?

oh ok for an A_3
|dw:1340595913293:dw|

|dw:1340595950507:dw|

The signs alternate

Like you take top entries

only the first row?

And take everything that isn't below that entry

like if its 10x10 u still only do the first row /?

For |A_4|
|dw:1340596049002:dw|

|dw:1340596102188:dw|

and you already know how to find the determinant for a 3 by 3

Same thing just take the top entries and do the signs alternating

yes just like i did above for the 3 by 3

But not all the top entries are 0

@eliassaab i dont really understnad wat u wrote

right...

See my example below and examine what is going on?

you have zeros. but what are you doing to the matrix?

Do you think he means to raise A to a power @eliassaab ?

Instead of finding the determinant ?

You raise it to the power 2, then 3, then 4.

You do not need to deal with determina

determinant

so can you start over with me?

what does a^n=0 even mean?

@myininaya, you do not need determinant to do that,

Yeah I know, but I'm asking you if I interpreted it correctly?