Question

2 -3 Find the eigenvalues and corresponding eigenvectors for the matrix -2 3 Selected Answer: 21 = 2, x1 = (-1, 1) 1.2 = 1. 12 = (3, 1) C.

Answer 1

1 Que - Bird the eigenvalues and coooresponding eigenvedtors for the madrix -3 3 Solution -3 het A= 3 -) AdI= 6:30) 2 Tard - 3 =) Adi = -4 3-d -3 (A-NI1 = 3-d

=) A-dil= (2-d)(3-d) - 6 = 1 A-dol= 6-Qd-3d +P - 6 =) IA-dila 50 Then characteristic equection of madix A in 18-d11c0 5dco = d (d-5)=0 =) dao cer d-5=0 a d=0,5 Let di=0 and da=5 Now, we find eșgenvestor corresponding to each eigenvale 34 het xz (1 be the eigenvedor corresponding to eigenvalue 0,20

183 = ax=d, X = AX = 0x AX=0 > -3 4 TJC] 3 st Applying Rg > Rg ta, we go 6:1703 2) 24 38820 - ) en MIN NOJ x2 in basis of eigen space corresponding to eigenadere ed=0

i X,= OR X= (32) 2 Again, let X= My be the eigenveton cosmesponding to eigenvalue do= 5 AX= dax AX= 5x (A-5 1 )X20 -3 [ I[] applying Rg & 2 l ) we get 2-3 -3 TI 31-[:] 0 0 -34- 3420

·3(4 + 2)20 -) x=-36 - NJ-03-[] :41]Y in the basis of eigenspace corresponding to eigenvalue da 25 . OR X2 = (1-1) Therefore dizo ,x=(3,2) da = 5 x2 = (1,-1)