Matrix Help (College Calculus II): Given A, find A^(30) [[-4][-2]]

[h2sbf7]

Hi all. Got an eigenvector matrix problem here. Problem is:

Let A = [4 -3]
~~~~~[2 -1]~~~~~(that's one matrix)

Find A³⁰[-4]
~~~~~[-2]~~~~~(again, one matrix

...without using a calculator.

So, obviously I start by solving for the eigenvalues. I take the determinant, factor, etc. and find that the eigenvalues are 1 and 2.

I then solve for the eigenvectors and get:

[ 1]
[-1]

for both. Then, to solve for the values of a1 and a2 in the next step, I add these to equations and get:

-4 = a1 - a2 and
-2 = a1 - a2 .

Doing elimination gets 0=2 in the bottom equation, which is useless to me.

What am I doing wrong?

 

[Ishuda]

Hi all. Got an eigenvector matrix problem here. Problem is:

Let A = [4 -3]
~~~~~[2 -1]~~~~~(that's one matrix)

Find A³⁰[-4]
~~~~~[-2]~~~~~(again, one matrix

...without using a calculator.

So, obviously I start by solving for the eigenvalues. I take the determinant, factor, etc. and find that the eigenvalues are 1 and 2.

I then solve for the eigenvectors and get:

[ 1]
[-1]

for both. Then, to solve for the values of a1 and a2 in the next step, I add these to equations and get:

-4 = a1 - a2 and
-2 = a1 - a2 .

Doing elimination gets 0=2 in the bottom equation, which is useless to me.

What am I doing wrong?

How sure are you about the eigenvectors? That is not what I get.