Consider
(what are the assumptions that you have forgotten to mention? And for good measure also consider )
.
Hello,
I'm a bit bloqued on a little demontration.
A^4=0 , (I-A)^-1 = I²+A+A²+A³
Here is what i've done:
I=(I-A).(I²+AI+A²I+A³I)
=> I=I³+AI²+A²I²+A³I³-AI²-A²I-A³I-(A^4)I
=> I=I+A²+A³-A²-A³-A^4
=> I=I-A^4
=> A^4=0
But it is prove in reverse...
The right way:
If you know that matrix A^4=0, how to prove that (I-A)^-1 = I²+A+A²+A³
But in ths case (harder I supose), I don't know how to do.
Can you help me?
Sorry but I have no particular assumptions.
The exercice is presented as such
A^4=0 , (I-A)^-1 = I²+A+A²+A³
It's already a problem for me at the base.
Or what do you mean?
If y consider (I-A).(I+A+A²+A³), I start in the same oposite direction that i've done no?
I still have a misanderstanding with this.
Hello, Adi0101!
I'm a bit bloqued on a little demontration.
Here is what I've done:
We have: .
Multiply by
. .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .
n . . . . . . . . . . .
But to prove it in reverse . . .
Just run the step in reverse . . .
We have: .
. . . . . . . . .
Add
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
Multiply by
. .
. . .