## Geometry and motion problem

Okay so I'm really stuck on this problem, have stared at it for a few hours and am quite desperate now. Does anyone have an idea?

Let A=( $a_{ij}$) be a symmetric nxn matrix, i.e. $a_{ij}=a_{ji}$ for all i,j in {i,...,n}. Define $f: R^{n} \rightarrow R$ by $f(\vec{x}) = \frac {1} {2} \vec{x}^{T} A \vec{x}$ , where the superscript T denotes transpose so that $f( x_{1} , ... , x_{n} ) = \frac {1} {2} \sum\limits_{i,j=1}^{n} a_{ij} x_{i} x_{j}$ . Show that $(\nabla f) (\vec{x}) = A (\vec{x})$ .