Find Matrix Eigenvalues ...
`[[3,2,4],[2,0,2],[4,2,3]]`

Solution:
`|A-lamdaI|=0`

`(3-lamda)`   `2`   `4`   `2`   `(-lamda)`   `2`   `4`   `2`   `(3-lamda)`

= 0

`:.(3-lamda)((-lamda) × (3-lamda) - 2 × 2)-2(2 × (3-lamda) - 2 × 4)+4(2 × 2 - (-lamda) × 4)=0`

`:.(3-lamda)((-3lamda+lamda^2)-4)-2((6-2lamda)-8)+4(4-(-4lamda))=0`

`:.(3-lamda)(-4-3lamda+lamda^2)-2(-2-2lamda)+4(4+4lamda)=0`

`:. (-12-5lamda+6lamda^2-lamda^3)-(-4-4lamda)+(16+16lamda)=0`

`:.(-lamda^3+6lamda^2+15lamda+8)=0`

`:.-(lamda+1)(lamda+1)(lamda-8)=0`

`:.(lamda+1)=0 or (lamda+1)=0 or (lamda-8)=0`

`:.lamda=-1 or lamda=-1 or lamda=8`

`:.` The eigenvalues of the matrix `A` are given by `lamda=-1,8`

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