Question

5. (a) State the Spectral Theorem for Symmetric matrices. (b) Write out the spectral factorization of =(22 (c) Using the change of variables x Qy, where Q is an appropriate orthogonal matric, express the quadratic form 5ri + 4r1t2 2 in terms of yi and y2. Describe and sketch the graph of the equation 5xi +4z1t2 +22 1 in the z1, z2 plane (d) Find the spectral decomposition of A.

Answer 1

mene osye ne.cessty okgoa Q

12 -1 9 2 -릎 wrax 지.oene. (:).*.(:5 ス2-

S)-22 6-u0 2 , e con esemo okeろxe.ee 91 m mond ges 啤. 6

4,9)- うえ bo ak,吩.ess-tnese esenspaCo TE VS