Find Eigen vectors for the following Find Eigen vectors for the following A = [1

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x.Hth="40" span="11" style="width:30pt"> A= 1 1 3 1 5 1 3 1 1 A-LI= 1-L 1 3 1 5-L 1 3 1 1-L |A-LI|=0= =[1-L][(5-L)(1-L)-1]-[1-L-3]+3[1-3(5-L)]=0 =L^3-7L^2+36=0 L=3,DIVIDING WITH L-3 ,WE GET   L^2-4L-12=0=[L-6][L+2] L=6 AND -2 HENCE EIGEN VALUES ARE L=-2,3,6 FOR L=-2 , EIGEN VECTORS ARE GIVEN BY [A+2I]X=0 [A+2I]= 3 1 3 X 0 1 7 1 * Y = 0 3 1 3 Z 0 3X+Y+3Z=0………………………………………1 X+7Y+Z=0…………………………………2 3*EQN.2-EQN.1 GIVES 20Y=0…..PUTTING IN EQN.1 , WE GET …..Z=-X SO EIGEN VECTOR IS [1,0,-1] FOR L=3 , EIGEN VECTORS ARE GIVEN BY [A-3I]X=0

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