Do both parts to get upvote .

(a) Let D be a square matrix and y an eigenvector with eigenvalue A. Prove that y is a solution to D'y +aDy + by = 0 if and only if A is a solution to x2 + ax + b = 0. (b) If 1 and 12 # 1 are eigenvalues of the square matrix D, with eigenvectors y1 and y2 respectively, use part (a) to show that v = Ay1 + By2 is an eigenvector of D2 - (1 + 12)D with eigenvalue -X12, for all A, BER