Find the symmetric matrix for the given quadratic form, $Q = 2x_1^2 + 2x_2^2 + 5x_3^2 – 3x_1 x_2+7x_3 x_1.$

Question

Accepted Answer

$\begin{bmatrix} 1 & \frac{-3}{2} & \frac{7}{2} \ \frac{-3}{2} & 2 & 0 \ \frac{7}{2} & 0 & \frac{5}{2}\end{bmatrix} $

Answer

$\begin{bmatrix} 1 & \frac{-7}{2} & \frac{3}{2} \ \frac{-7}{2} & 2 & 0 \ \frac{3}{2} & 0 & \frac{5}{2}\end{bmatrix} $

Answer

$\begin{bmatrix} 1 & \frac{3}{2} & \frac{-7}{2}\ \frac{3}{2} & 2 & 0 \ -\frac{7}{2} & 0 & \frac{5}{2}\end{bmatrix} $

Answer

$\begin{bmatrix} 1 & \frac{-3}{2} & \frac{7}{2} \ \frac{-3}{2} & 2 & 0 \ \frac{7}{2} & 0 & 5\end{bmatrix} $

Find the symmetric matrix for the given quadratic form, \(Q = 2x_1^2 + 2x_2^2 + 5x_3^2 – 3x_1 x_2+7x_3 x_1.\)