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The Gershgorin set for an $n\times n$ complex matrix $A=(a_{ij})$ is a collection of disks in the complex plane centered at $a_{11},a_{22},\dots,a_{nn}$ which are guaranteed to contain all the eigenvalues of $A$.

If... the Gershgorin set of a $5\times 5$ matrix $A$, we can say that:


$A$ is invertible


$A$ is singular (not invertible)


One cannot tell if $A$ is invertible or not

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