Question

: Linear Algebra: Let A be an nxn matrix and let B = I - 2A + A^2. Let x be an eigenvector of A corresponding to an eigenvalue L, and that same x also be an eigenvector of B corresponding to an eigenvalue U, i.e. Ax = Lx and Bx = Ux. Show that if L = 1 is an eigenvector of A, then the matrix B will be singular.

Answer 1

Also note that U = 1 - 2L + L^2, as shown in an earlier part of the problem (see OpenStudy question before this).

Answer 2

Sorry, I got it.