Question

(7') Orthogonally diagonalize the matrix (4 12). 1

Answer 1

4 I orthogonally diagonalize the matrise sols The characteristic equation of the giren is 4- -2 = - 1-> matrise (4-3) = 0 2 (4-7) (1-7) – 4 =0 4-42-2+2-450 2-5 co 70-5) = 7, 70 and 12=5 The eigen rector corresponding to 7,20 be found (A-1,1)=(4-0.-2 The eigenvalues eܒܘ PS to J-4*] 2 1-0 now peonform row operations to obtain the row reduced echleon form of the above metrise 4 -Y - (silent - Conte] RR₂ +2R,

Now Salve the matrix ecuation [: 7] (21-6:] a-k veco a, =%dz let dat "" -[**]8374 so Pigen rector corresponding Vi = yt to eigen value * to eigen Now, find eigen rector Corresponding value +2=5 (4-5 (A-24) (* 1-5 2 -4 pear form row operations to obtain the row reduced echleon form of the above matrise -1 -2 → > -4 R,R, xG1) R> R+ R, Now Solare for the matrix equation 6 :JU)-1] Wp+2l=0 Va= -2V2

Let ♡=t, then ,=-zt V2 = (129-130) + 72=5 is V2 = so, the ergen Vector Corresponding to eigen value [] The diagonal matrise (the diagonal entries are the ergen values -2,72): potes the matrise with the eigen rectors (VV₂) s its calumas y P= and p' = alth Man thanh ·A= PDP-1 So 2/5 415 4 11-14 : ] -% 2