Find the Matrix of the Quadratic Form $$4 x _ { 1 } ^ { 2 } + 5 x _ { 2 } ^ { 2 } + 3 x _ { 3 } ^ { 2 } - 4 x _ { 1 } x _ { 2 } + x _ { 2 } x _ { 3 }$$

Multiple Choice

Find the matrix of the quadratic form.
- $$4 x _ { 1 } ^ { 2 } + 5 x _ { 2 } ^ { 2 } + 3 x _ { 3 } ^ { 2 } - 4 x _ { 1 } x _ { 2 } + x _ { 2 } x _ { 3 }$$

A)
$\left[ \begin{array} { c r c } 4 & - 2 & 1 / 2 \\ - 2 & 5 & 0 \\ 1 / 2 & 0 & 3 \end{array} \right]$

B)
$\left[ \begin{array} { r r r } 4 & - 2 & 0 \\ - 2 & 5 & 1 / 2 \\ 0 & 1 / 2 & 3 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 4 & - 4 & 0 \\ - 4 & 5 & 1 \\ 0 & 1 & 3 \end{array} \right]$

D)

$\left[ \begin{array} { l l l } 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 3 \end{array} \right]$