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Problem: eigenvalues [[8,-6,2],[-6,7,-4],[2,-4,3]] [ Calculator, Method and examples ]

Solution:
Your problem -> eigenvalues [[8,-6,2],[-6,7,-4],[2,-4,3]]

|A-lamdaI|=0

 (8-lamda) -6 2 -6 (7-lamda) -4 2 -4 (3-lamda)
= 0

:.(8-lamda)((7-lamda) × (3-lamda) - (-4) × (-4))-(-6)((-6) × (3-lamda) - (-4) × 2)+2((-6) × (-4) - (7-lamda) × 2)=0

:.(8-lamda)((21-10lamda+lamda^2)-16)+6((-18+6lamda)-(-8))+2(24-(14-2lamda))=0

:.(8-lamda)(5-10lamda+lamda^2)+6(-10+6lamda)+2(10+2lamda)=0

:. (40-85lamda+18lamda^2-lamda^3)+(-60+36lamda)+(20+4lamda)=0

:.(-lamda^3+18lamda^2-45lamda)=0

:.-lamda(lamda-3)(lamda-15)=0

:.lamda=0 or(lamda-3)=0 or(lamda-15)=0

:. The eigenvalues of the matrix A are given by lamda=0,3,15,

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