Hi, I need help for this problem: Find the eignevalues and eingenvectors for the matrix below. DO NOT compute them directly by computing the matrix: A-1 We need to find some kind of demonstration to see if the eignevalues of A-1 are the same, opposite or inverse (or whatever) as those of matrix A Suppose that the eignvalues are 1,2,3 and the eignvectors are [1,1,0], [0,1,0],[ 3,-1,2] ( in columns) Does someone has any idea?? Thank you B

Hi, I am afraid it is too late to answer this question as it was posted a month ago. But just in case. The eigenvectors will be the same but the eigenvalues will be the reciprocals of those for the original matrix (assuming A-1 is the inverse of A). It all follows from this simple computation: Ax = bx => A-1(Ax) = A-1bx => x = b A-1x => (1/b)x = A-1x (so x is an eigenvector of A with evalue 1/b) privided x is an eigenvector of A with eigenvalue b. Good luck. C-villain