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Let \(\displaystyle <x, x>=3x_{1}^2+2x_{2}^2+x_{3}^2-4x_{1}x_{2}-2x_{1}x_{3}+2x_{2}x_{3} \) be a quadratic form in V=R, where \(\displaystyle x=x_{1}e_{1}+x_{2}e_{2}+x_{3}e_{3}\) (in the base \(\displaystyle {e_{1},e_{2},e_{3}}\).

Find the inner product corresponding to this quadratic form.

Is this that easy that you have to change '' second'' x-es for y (for example to write \(\displaystyle 2x_{2}y_{3}\) instead of \(\displaystyle 2x_{2}x_{3}\) at the end), or what I have to do?

Find the inner product corresponding to this quadratic form.

Is this that easy that you have to change '' second'' x-es for y (for example to write \(\displaystyle 2x_{2}y_{3}\) instead of \(\displaystyle 2x_{2}x_{3}\) at the end), or what I have to do?

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