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Verify Cayley Hamilton theorem for the matrix A and hence ,find $A^{-1}$ & $A^4$ ,where $A = \begin{bmatrix} \ 1 & 2 & -2 \\ \ -1 & 3 & 0 \\ \ 0 & -2 & 1 \\ \end{bmatrix}$
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written 6.3 years ago by
teamques10
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• modified 6.0 years ago |
To verify C- H theorem characteristic eqn |A- λI| =0
i.e. $ \begin{vmatrix} 1-λ&2&-2 \\ -1&3-λ&0 \\ 0&-2&1-λ \end{vmatrix} = 0 $
Expanding we get a cubic equation in λ as $λ^3 - 5λ^2 + 9λ - 1 =0$
To verify C-H theorem we have to show that $A^3 - …
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