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Find all eigenvalues and their corresponding eigenspaces of the following matrix. A.( egin{pmatrix}3&0\ 1&2end{pmatrix} )

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Advance Math

Find all eigenvalues and their corresponding eigenspaces of the following matrix. A.( egin{pmatrix}3&0\ 1&2end{pmatrix} )

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Solution A eginpmatrix30 12endpmatrix let lambda in mathbbR be an eigenvalue of A Then We have Axlambda x lambda in mathbbR2 xeginpmatrixx1 x2endpmatrixin mathbbR2 x eq 0 iff Axlambda x0 iff iggAlambda Iiggx0 hspace2mm iggx eq 0igg implies Alambda I lefteginpmatrix30    See Answer
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