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Determine the value of a so that ( lambda = 2 ) is an eigenvalue...

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Advance Math

Determine the value of a so that ( lambda = 2 ) is an eigenvalue of 

( A=egin{pmatrix}1&-1&0\ a&1&1\ 0&1+a&3end{pmatrix} )

Then show that A is diagonallizable and diagonalize it. 

Answer & Explanation Solved by verified expert
3.6 Ratings (451 Votes)
Solution we have A2Ieginpmatrix110 a11 01a3endpmatrix Then if lambda 2in SPA implies A2Ieginvmatrix110 a11 01a3endvmatrix0 Thus a1 we have Aeginpmatrix110 111 003endpmatrix implies PlambdaAlambda Ieginvmatrix1lambda 10 11lambda 1 003lambda endvmatrix    See Answer
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