(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello and thanks again to anyone who has replied my posts. Your help is a great deal and really appreciated.

I have the following homework question which I have answered and I want a comment if it is valid or illogical:

We are given a matrix, with eigenvalues 3 and 7 respectively.

We are asked to say if there other matrices with the same eigenvalues and if the set containing all these matrices is finite.

2. Relevant equations

the matrix given:

2 1

-5 8

3. The attempt at a solution

I have thought of the following answer: My point is that there are infinite matrix with the same eigenvalues that have different eigenvectors. So I say that the linear system:

A(x1,y1)=λ1(x1,y1)

A(x2,y2)=λ2(x2,y2)

where A is a 2x2, has infinite solutions IF we take a11,a12,a21,a22(the elements of the matrix) as the variables of the linear system. The solutions will have x1,y1 and x2,y2 as constant parameters.

Have i got something terribly wrong?

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# Matrices and eigenvalues. A comment in my answer.

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