The given quadratic form is:
\[ 3x_1^2 + x_2^2 + 2x_3^2 - 2x_1x_3 + 2kx_2x_3 \]
This can be expressed in matrix form as:
\[ \mathbf{x}^T A \mathbf{x} \]
where \(\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\) and \(A\) is the symmetric matrix
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