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1. （解答题）写出下列二次型的矩阵，并求它们的秩.
(1)

f_{1} = 3 x_{1}^{2} + 2 x_{2}^{2} - x_{3}^{2} + 2 x_{1} x_{2} - 4 x_{2} x_{3}

.
(2)

f_{2} = x_{1}^{2} - 2 x_{1} x_{3}

.
(3)

f_{4} = [\begin{array}{lll} x_{1} & x_{2} & x_{3} \end{array}] [\begin{array}{lll} 1 & 4 & 3 \\ 2 & 2 & 6 \\ 1 & 0 & 3 \end{array}] [\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}]