(Solved): (2 points) All vectors are in Rn. Check the true statements below: A. If u2+v2=u+v ...

(2 points) All vectors are in ${\mathbb{R}}^n$. Check the true statements below: A. If $\Vert u{\Vert }^2+\Vert v{\Vert }^2=\Vert u+v{\Vert }^2$, then $u$ and $v$ are orthogonal. B. $u\cdot v-v\cdot u=0$. C. For any scalar $c,\Vert cv\Vert =c\Vert v\Vert$. D. If $x$ is orthogonal to every vector in a subspace $W$, then $x$ is in $W^{\perp }$. E. For an $m\times n$ matrix $A$, vectors in the null space of $A$ are orthogonal to vectors in the row space of $A$.