is htis matrix diagonalizable?(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \left( \begin{array}{ccc}4&0&0\\0&2&2\\2&3&1 \end{array} \right) [/tex]

the characteristic polynomial is [tex] (x+1)(x-4)^2 [/tex]

whats worng with the multiplicity here?

the back of the book says dim(E4) =1 and here multiplicity is 2?

but what about this problem

[tex] \left( \begin{array}{ccc}3&0&6\\0&-3&0\\5&0&2 \end{array} \right) [/tex]

whose characteristic polynomial is [tex] (\lambda +3)^2 (\lambda -8) = C_{A} (x) [/tex]

here the multiplicity of lambda = -3 is 2 and the [itex] dim(E_{-3}) = ??

what is the dimension of E (-3)??

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# Homework Help: Is this matrix diagonalizable?

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