Here I found options 2 & 3 to be false. Its answer is option d .How come A is diagonalizable? And how minimal polynomial is not equal to characteristic eqn . Please explain.
query on diagonalizabiblity of a matrix
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linear-algebra
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1all symmetric (real) matrices are diagonalizable – 2017-01-31
1 Answers
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The characteristic polynomial of $A$ is $\chi(\lambda)=\lambda^2(\lambda-3a)$. Being $A$ diagonalizable, its minimum polynomial is necessarily $\mu(\lambda)=\lambda^1 (\lambda-3a)^1$ if $a\ne 0 $ and $\mu(\lambda)=\lambda^1$ if $a=0$ so, $\mu(\lambda)\ne \chi(\lambda).$