Hamilton Campbell
08/27/2024 · Senior High School
Bxpress the quadric form \( f(x, y)=3 x^{2}+2 x y+6 y^{2} \) in matrix form, \( f(\vec{x})=\vec{x}^{T} A \vec{x} \) where where \( \vec{x}=\left(\begin{array}{l}x \\ y \\ z\end{array}\right) \).
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The matrix \( A \) for the quadratic form \( f(x, y) = 3x^2 + 2xy + 6y^2 \) is:
\[ A = \begin{pmatrix} 3 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 0 \end{pmatrix} \]
And the matrix form of the quadratic form is:
\[ f(\vec{x}) = \vec{x}^T A \vec{x} \]
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