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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. `[[3,2,4],[2,0,2],[4,2,3]]`
3. `[[1,1,1],[-1,-3,-3],[2,4,4]]`
4. `[[1,2,3],[0,1,0],[2,3,1]]`
5. `[[1,2,1],[6,-1,0],[-1,-2,-1]]`
6. `[[6,-2,2],[-2,3,-1],[2,-1,3]]`
7. `[[2,3],[4,10]]`
8. `[[5,1],[4,2]]`
9. `[[6,3],[4,5]]`
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Example1. 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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