Teaching DSSSB TGT Mock Test 2025 Engineering Mathematics Linear Algebra Eigenvalues

If the eigenvalues of the matrix \( \begin{pmatrix} x & 1 \\ 1 & y \\ \end{pmatrix}\) are in the ratio 3 ∶ 1 when y = 2, then x = ?

1
2,\(\frac{14}{3}\)
2
\(\frac{1}{2},\frac{1}{6}\)
3
14, 6
4
6, 2
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