Find Matrix Eigenvalues ...
`[[1,1,1],[-1,-3,-3],[2,4,4]]`

Solution:
`|A-lamdaI|=0`

`(1-lamda)`   `1`   `1`   `-1`   `(-3-lamda)`   `-3`   `2`   `4`   `(4-lamda)`

= 0

`:.(1-lamda)((-3-lamda) × (4-lamda) - (-3) × 4)-1((-1) × (4-lamda) - (-3) × 2)+1((-1) × 4 - (-3-lamda) × 2)=0`

`:.(1-lamda)((-12-lamda+lamda^2)-(-12))-1((-4+lamda)-(-6))+1((-4)-(-6-2lamda))=0`

`:.(1-lamda)(-lamda+lamda^2)-1(2+lamda)+1(2+2lamda)=0`

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

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

`:.-lamda^2(lamda-2)=0`

`:.lamda^2=0 or (lamda-2)=0`

`:.lamda=0 or lamda=2`

`:.` The eigenvalues of the matrix `A` are given by `lamda=0,2`

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