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?