Let $V$ be a finite-dimensional vector space and $\beta$ be a bilinear form. According to the definition of the bilinear forms is possible to do the following: $$\begin{align}\beta(u,v)&=\beta(u+w-w,v)=\beta(u+w,v)-\beta(w,v)\\ &=\beta(u+w,v)+\beta(w,-v)=\beta(u+2w,v-v)\\ &= \beta(u+2w,0)=0\end{a...