Question 1 a) Using the matrix Q 1 1 2 -2 2 2 i) calculate A = Q'Q (3) ii) determine eigenvalues and normalized eigenvec

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Question 1 A Using The Matrix Q 1 1 2 2 2 2 I Calculate A Q Q 3 Ii Determine Eigenvalues And Normalized Eigenvec 1 (274.81 KiB) Viewed 20 times

Question 1 a) Using the matrix Q 1 1 2 -2 2 2 i) calculate A = Q'Q (3) ii) determine eigenvalues and normalized eigenvectors of A and use them as columns of matrix C. [8] iii) show that C'AC = D, where D is diagonal with eigenvalues of A in the diagonal iv) calculate B = QQ'. Determine the eigenvalues of B, compare them with eigenvalues of A in ii) and comment. (6) b) Let A :pxp be a non-singular matrix with eigenvalues 11, 12,..., p. Show that i) A = I1=1 / ii) trA = Slidi [2] [2]