<p>First show that $V^\prime\subseteq V$. Since every vector of $R^\prime$ is in $R$, any vector we can construct in $V^\prime$ as a linear combination of vectors from $R^\prime$ can also be constructed as a vector in $V$ by the same linear combination of the same vectors in $R$. That was easy, now turn it around.</p>

-<p>Next show that $V\subseteq V^\prime$. Choose any $\vect{v}$ from $V$. Then there are scalars $\alpha_1,\,\alpha_2,\,\alpha_3,\,\alpha_4$ so that

+<p>Next show that $V\subseteq V^\prime$. Choose any $\vect{v}$ from $V$. So there are scalars $\alpha_1,\,\alpha_2,\,\alpha_3,\,\alpha_4$ such that

## src/section-LDS.xml