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Solution
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Solution provided by AtoZmath.com
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Matrix Eigenvalues calculator
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 1. `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
2. `[[6,-2,2],[-2,3,-1],[2,-1,3]]`
3. `[[3,2,4],[2,0,2],[4,2,3]]`
4. `[[1,1,1],[-1,-3,-3],[2,4,4]]`
5. `[[2,3],[4,10]]`
6. `[[5,1],[4,2]]`
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Example1. `[[8,-6,2],[-6,7,-4],[2,-4,3]]`
Find eigenvalues ...
`|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`
`:.` the eigenvalues of the matrix A are given by `lamda=0,3,15`
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