Suppose that A and B are two nxn matrices and that is an eigenvector for A with corresponding eigenvalue 5 and x is also an eigenvalue for B but corresponding to the eigenvalue 7. Show that 12 is an eigenvalue of A+B Solution If x is an eigenvector for A (B) corresponding to eigenvalue 5 (7), then Ax=5x and Bx=7x Then (A+B)x=Ax+Bx=5x+7x=12x So 12 is eigenvalue of A+B.