Question

Find the eigenvalues of the given matrices

17. 21] 4t

Property 2 A matrix is singular if and only if it has a zero eigenvalue

Answer 1

Let A = 2t 4t H - 22 is ginen by Then chiean of A det (A-22=0 X 22 - 2t 4t-) E -> (42-?) + 4t (1=2+) = 0 = 1=24, 27 The Eigen-values are 24, 2 26. 42x + 44²

3 6 Ginen 2 =) 7 2 chean of A given by 6 . -X det A-df) to a -1 2-4-1 7-8 using co=C3² 2 262 3 1- - 1 -1-1212.17 7-x-2 2 using RN 3. O Ro=R3+2 R2 Cam -1 2-1 22-5 5-) CS

l-d 3 - 1 2- 2-5 5-7 2 3 [A-5) 2(23-02) M o (1–17 [CA-5) (4-2) –(21-5)] =(1-12 [**=+* 7/+10-28+] -3[ 5-31] (1-2) (97-99 +5 ) +63(31-5)=0 1291 +385 --?+ 9/?=154+1-4- - 3+ lod -15%8f to tak zsdtlost o 3 2 د) door, lod 7151=d -10/+15 slodt15) = Xlo dit is = x = 10 + 100-60 А Therefore the Eign-values of A. 2 lo 1 2 To 5 + 110 are o stvo 1 3 - & A= 2 2:1 7 & Ergen-value -value ob S det A= 15-3(-5) + 6(-5) 30-30=0 Hence A is singular ear & Ann lomyshoi CS CamScanner Yemen