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Home > Matrix & Vector calculators > Inverse of matrix using Cayley Hamilton method example
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3. Cayley Hamilton method example
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- Example `[[3,1,1],[-1,2,1],[1,1,1]]`
- Example `[[2,3,1],[0,5,6],[1,1,2]]`
- Example `[[2,3],[4,10]]`
- Example `[[5,1],[4,2]]`
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Other related methods
- Adjoint method
- Gauss-Jordan Elimination method
- Cayley Hamilton method
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2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example) | 4. Example `[[5,1],[4,2]]`
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3. Example `[[2,3],[4,10]]`
Find Inverse of matrix using Cayley Hamilton method
`A=[[2,3],[4,10]]`
Solution:
To apply the Cayley-Hamilton theorem, we first determine the characteristic polynomial p(t) of the matrix A.
`|A-tI|`
`=(2-t) × (10-t) - 3 × 4`
`=(20-12t+t^2)-12`
`=t^2-12t+8`
`p(t)=t^2-12t+8`
The Cayley-Hamilton theorem yields that
`O = p(A)=A^2-12A+8I`
Rearranging terms, we have
`:. -8I = A(A-12I)`
`:. A^-1 = 1/-8(A-12I)`
Now, first we find `A-12I`
Now, `A^-1 = 1/-8(A-12I)`
This material is intended as a summary. Use your textbook for detail explanation.
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2. Example `[[2,3,1],[0,5,6],[1,1,2]]`
(Previous example) | 4. Example `[[5,1],[4,2]]`
(Next example) |
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