Eigenvalue Identification in Structured Matrices

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Consider a 3×3 matrix \(M\) where every diagonal entry is \(r\) and every off-diagonal entry is \(c\). Determine all eigenvalues of \(M\) in terms of \(r\) and \(c\).

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Hint

Recall that for an \(n\times n\) matrix with constant diagonal and off-diagonals, one eigenvalue is \(r+(n-1)c\) while the others are \(r-c\).

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\(\lambda_1 = r+2c, \lambda_2 = r-c\) (with multiplicity 2)

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Eigenvalue Identification in Structured Matrices

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Eigenvalue Identification in Structured Matrices

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