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Let A be a square matrix defined by ( A=egin{pmatrix}4&-2&1\ 2&0&1\ 2&-2&3end{pmatrix}hspace{2mm} )Find the minimal...

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Advance Math

Let A be a square matrix defined by ( A=egin{pmatrix}4&-2&1\ 2&0&1\ 2&-2&3end{pmatrix}hspace{2mm} )Find the minimal polynomial of A. Then express ( A^4 ) and ( A^{-1} ) in terms of A and I.

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Solution we have Aeginpmatrix421 201 223endpmatrix The characteristics polynomial is Plambdaigglambda3S1lambda2S2lambdas3igg ullet S1trA4037 ullet S2eginvmatrix42 20endvmatrixeginvmatrix01 23endvmatrixeginvmatrix41 23endvmatrix421016 ullet S3eginvmatrix421 201    See Answer
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