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# FP2 Eigenvectors with an unknown element in 2x2 matrix. watch

1. Hello,

I am currently in need of assistance on the first part of the question below.

I have found both eigenvalues to be:

Lambda = k

Lambda = 2

How would I go about finding the eigenvectors? Would they have to be in terms of k?
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2. (Original post by Wunderbarr)
Hello,

I am currently in need of assistance on the first part of the question below.

I have found both eigenvalues to be:

Lambda = k

Lambda = 2

How would I go about finding the eigenvectors? Would they have to be in terms of k?
Well, one eigenvector is easy enough.

It's

And the other will be in terms of , as you rightly said:

3. am I too late today?
4. (Original post by Zacken)
x
(Original post by TeeEm)
x
Could either of you or someone else post some sort of help/guidance for finding the eigenvector for either eigenvalue?

Assuming I don't know anything, as my method of multiplying the matrix M by the 2x1 matrix (x, y) isn't currently working for me
5. (Original post by Wunderbarr)
Could either of you or someone else post some sort of help/guidance for finding the eigenvector for either eigenvalue?

Assuming I don't know anything, as my method of multiplying the matrix M by the 2x1 matrix (x, y) isn't currently working for me
I am not an expert but I can only find one eigenvector for lamda = 2
6. (Original post by Wunderbarr)
Could either of you or someone else post some sort of help/guidance for finding the eigenvector for either eigenvalue?

Assuming I don't know anything, as my method of multiplying the matrix M by the 2x1 matrix (x, y) isn't currently working for me
Multiply out the matrix with the vector. Then you have two equations in x and y, so you can find y in terms of x.
7. (Original post by Wunderbarr)
Could either of you or someone else post some sort of help/guidance for finding the eigenvector for either eigenvalue?

Assuming I don't know anything, as my method of multiplying the matrix M by the 2x1 matrix (x, y) isn't currently working for me
Let's work with the first one:

and , so we're good here; can take any value, pick one.
8. (Original post by Zacken)
Let's work with the first one:

and . Plug this back into the first equation: .

So our eigenvector is any multiple of assuming I haven't made a silly algebraic mistake somewhere.
So where did the 2y = 2k come from? :3
9. (Original post by Wunderbarr)
So where did the 2y = 2k come from? :3
Do you remember your matrix multiplication rules?

10. (Original post by Zacken)
Do you remember your matrix multiplication rules?

Yesss I do, except I don't seem to be getting it anywhere.

Anyway I seem to have figured something out and got (1, 0) for the other eigenvector.
11. (Original post by Wunderbarr)
Yesss I do, except I don't seem to be getting it anywhere.

Anyway I seem to have figured something out and got (1, 0) for the other eigenvector.
Correctomundo. (I think we actually have for any , but yours is as good as any, somebody will jump in and correct me if I'm wrong).
12. (Original post by Wunderbarr)
So where did the 2y = 2k come from? :3
Right, sorry about that. The woes of grogginess. That was completely wrong.

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