(1) This question deals with deflation of eigenvalues/vectors from matrices. You are given the matrix 309 228 -240 A= 60 -117 510/49, 12 6 298 and are told that the vector v = (-8 10 9)' is an eigenvector of A (which you are surely able to check!) (i) Deflate v from A. (ii) Find (say, directly) the eigenvectors of the 2X2 deflated matrix. (iii) Use (ii) is order to find an eigenbasis of A to R3 (i.e., a basis for R* made of eigenvectors of A). (iv) Diagonalize A, i.e., write it in the form PDP-1. (v) Triangularize A, i.e., find an orthogonal Q and an upper triangular U such that A = QUQ'. Make sure to carefully show your work! Note: You may use Matlab in order to invert P. FYI: In general, you may find the jth column of the inverse of a matrix B by solving the equation Ba = ;. So, for finding the inverse, you need to solve m such equations. However, you need to factor B only once, so the total cost will still be 0(m3) (why?) (1) This question deals with deflation of eigenvalues/vectors from matrices. You are given the matrix 309 228 -240 A= 60 -117 510/49, 12 6 298 and are told that the vector v = (-8 10 9)' is an eigenvector of A (which you are surely able to check!) (i) Deflate v from A. (ii) Find (say, directly) the eigenvectors of the 2X2 deflated matrix. (iii) Use (ii) is order to find an eigenbasis of A to R3 (i.e., a basis for R* made of eigenvectors of A). (iv) Diagonalize A, i.e., write it in the form PDP-1. (v) Triangularize A, i.e., find an orthogonal Q and an upper triangular U such that A = QUQ'. Make sure to carefully show your work! Note: You may use Matlab in order to invert P. FYI: In general, you may find the jth column of the inverse of a matrix B by solving the equation Ba = ;. So, for finding the inverse, you need to solve m such equations. However, you need to factor B only once, so the total cost will still be 0(m3) (why?)