What is A^n for Matrix A = k+1, k-1?

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Homework Help Overview

The discussion revolves around finding the expression for A^n where A is a 2x2 matrix defined in terms of a variable k. Participants are exploring the relationship between the matrix powers and the parameter k.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to derive a general formula for A^n based on specific values of k, with some expressing confusion about the relationship. There are inquiries about the multiplication of matrices and the implications of different k values on the matrix powers.

Discussion Status

The conversation includes attempts to clarify the problem and explore specific cases, such as k=3. Some participants have expressed that they have made progress in understanding the relationship for certain values of k, while others are still seeking a general solution.

Contextual Notes

One participant notes that the inquiry is not related to homework, despite the forum's guidelines suggesting otherwise. There are reminders about the forum's rules regarding posting homework questions.

ronicencen
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If I have a matrix A=
k+1_____k-1
k-1_____k+1

What would A^n for whatever value of k or n be? What's the relationship?

I only found something k=1 and 2 so far...(too confusing to type)
 
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I'm not sure what you're asking. Can you multiply two square matrices?

A^2 = AA
A^3 = AAA, etc.
 
Oh wait, I think I figured it out for separate k values... now I just need a general k to n relationship :S
 
If k=3, for example:
A= a;b
___c;dA^n= 2^(n-1)(a^n; b^n
_____________b^n; a^n)

a^n= 3^(n-2)a-2^(n-1)+1
b^n= 3^(n-2)b+2^(n-1)-1
 
Do not ask for help here with exercises! Go to the HW forum!

Read Sticky thread: Do not post homework questions here!

Are you blind? :-P
 
Actually it's not homework
I figured it out anyway...
 
but we ask for TUTORIALS here, not help with individual questions.
 

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