Question

please help asap

Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 1 18 12 -1 10 4 l; 2 = 3,4 1 -6 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 3 0 0 For P= D= 0 3 0 0 0 4 OB. 300 For P = D = 0 4 0 0 0 4 O C. The matrix cannot be diagonalized.

Answer 1

let A= 18 12 10 4 - 6 0 characteristic eq of A is 1 A-d Il=0 I-d 12 lord So 4. -d -0 (1-0) [-1610-d) + 24) - 18[ 1-4) +12 [6+1-10] =0 (1-1) [ 12-100+24] -18 [d-4] +12[1-4] = (1-d) (4-6) (d- 4-18 (-4) + 12 (d-4) = 0 = (d-4) [_d2 + 7d-6 - 18 +12] =o. је (7-4) (-12 +41 - 12) = 0 - d2+7d-12=0 d=4 d²-7 dt 120 = (d-u) (d-3)=0 =) d=39 4 (repeated twice) So, D= is the diagonal mateix of eigenvalues of A. d-40 3 O 04 o оо u we Know For d=3 74 Now matrix l is matrix of eigerrectors. consider (A-31) X- 18 127 7 - 6 B Reducing matórix F-2 12 Rtf - 2 R2 4 4 RR-YR3 7 - 6 - 3 0 1 JE Jo -3 o 18 7 -) 4 Rz7 Rg tR2 u 7 Y 7 % =o 2 -o X₂ t=0 and – 4 + 7 + 4z = x = -38% = = -&

sol is the BE]alipoecon for me 37 where az is arbitrary. So, elgenrector for d = 3. A-41) X=0 For de 4 consider 18 12 이 6 J & B - 6 -4 こ。 х 6 - 682 & 4oz 4= 64 +488 ol} where ☆ & are soy ht h % arbitrary,

Soj [] 4. to ng So, option (A) is correct. are the edgesrectors elgesrectors correspondi A.M= G.M A is diagonali zable. Also as 80 let p = -3 0 6 O Y 3 and D O 4 o - -1 0 o 0