Matrix Algebra (Recurrences & Diagonalisation)

[Dick]

Oh damn, so it does.

So I'll have :


[cn dn] = 6*A^n[3 1] -3 *A^n[1 -4]

as the expression for cn & dn? or should they be seperate?

I'm guessing separate since it asks for a ratio in part b)

Keep going. You know expressions for A^n[3,1] and A^n[1,-4]. Then equate the components to find cn and dn separately.

 

[ShaunDiel]

UGH, I'm pretty sure I messed up way back around the start.

http://www.wolframalpha.com/input/?i=[[1%2F143*67%2C1%2F143*33]%2C[1%2F143*44%2C-1%2F143*54]]

My eigenvalues are right, but 1 vectors wrong.

 

[ShaunDiel]

Keep going. You know expressions for A^n[3,1] and A^n[1,-4]. Then equate the components to find cn and dn separately.

Okayy, So I'lll have:

[Cn, dn] = 6 (6/11)^n *[3 1] - 3 (-5/11)^n * [1 -4]

What do you mean by equate components?

 

[Dick]

You have a vector equal to a vector. They are equal if each element of one vector is equal the the corresponding element of the other vector. So cn=?? You know, I really don't think are are so bad at this, you found the eigenvectors easily and found the eigenvalues without much trouble. I don't know why you are checking back for approval of basic things so often. The next question that comes up, why don't you try and imagine what I would answer and then jump to the next step?