Find Matrix Eigenvalues ...
`[[8,-6,2],[-6,7,-4],[2,-4,3]]`

Solution:
`|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`

`:.lamda=0 or lamda=3 or lamda=15`

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

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