5' Denition. A generalized eigenvector of grade g of the square matrix A corresponding to the eigenvalue /1 is a vector p that satises: (i) (A 1103p = 0, and (ii) (A ADS1p #5 0. (a) Using this denition prove: Theorem. If g is a generalized eigenvector of grade g + 1 of the matrix A corresponding to the eigenvalue x1, and if 3 satises (A - 210a = y. then 3 is a generalized eigenvector of grade 3. (b) Assume that A and B are similar, matrices (i.e., assume that there exists an invertible matrix P such that P'IAP : B). Assume also that 11 is an eigenvalue of A with generalized eigenvector E of grade g. Give an expression for a generalized eigenvector of grade 3 for the matrix B as a function of E and P, and using the denition of generalized eigenvector of grade 3, prove that the vector you found is a generalized eigenvector of grade g for B