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there is

[tex]

A\epsilon M_{2x2}(Q)

[/tex]

I am given that A is diagonazable

prove that

A)

[tex]

A^{10}+12A

[/tex]

is diagonizable too

B)give an example for a matrix[tex] B\epsilon M_{2x2}(Q)[/tex]

that is not diagonizable,but b^2 is diagonisable

??

i know that the eigenvalues of a matrix are the same as for every matrix

like A^10 or A^3+2A+3I etc..

but i dont now how to show what they ask

??

[tex]

A\epsilon M_{2x2}(Q)

[/tex]

I am given that A is diagonazable

prove that

A)

[tex]

A^{10}+12A

[/tex]

is diagonizable too

B)give an example for a matrix[tex] B\epsilon M_{2x2}(Q)[/tex]

that is not diagonizable,but b^2 is diagonisable

??

i know that the eigenvalues of a matrix are the same as for every matrix

like A^10 or A^3+2A+3I etc..

but i dont now how to show what they ask

??

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