## Question

###### Without computing them, prove that the eigenvalues of the matrix $$ A=\left[\begin{array}{rrr} 6 & 2 & 1 \\ 1 & -5 & 0 \\ 2 & 1 & 4 \end{array}\right] $$ satisfy the inequality $1 \leq|\lambda| \leq 9$.

Without computing them, prove that the eigenvalues of the matrix $$ A=\left[\begin{array}{rrr} 6 & 2 & 1 \\ 1 & -5 & 0 \\ 2 & 1 & 4 \end{array}\right] $$ satisfy the inequality $1 \leq|\lambda| \leq 9$.

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