Constructing bases (worked out, please check )

[sid9221]

http://dl.dropbox.com/u/33103477/Union.png

Omiting zeroes because they add nothing:

\begin{bmatrix}<br /> 3 &amp; 1 &amp; 7 &amp; 4\\ <br /> 5 &amp; 6 &amp; 7 &amp; 3<br /> \end{bmatrix}

RREF

\begin{bmatrix}<br /> 1 &amp; 0 &amp; \frac{35}{13} &amp; \frac{21}{13}\\ <br /> 0 &amp; 1 &amp; \frac{-14}{13}&amp; \frac{-11}{13}<br /> \end{bmatrix}

Hence the basis is:
<br /> \begin{Bmatrix}<br /> \frac{-35}{13}\\ <br /> \frac{14}{13}\\ <br /> 1\\ <br /> 0<br /> \end{Bmatrix}, \begin{Bmatrix}<br /> \frac{-21}{13}\\ <br /> \frac{11}{13}\\ <br /> 0\\ <br /> 1<br /> \end{Bmatrix}Similarly,

\begin{bmatrix}<br /> 6 &amp; 4 &amp; 3 &amp; 6\\ <br /> 4 &amp; -1 &amp; 3 &amp; 7<br /> \end{bmatrix}<br />

RREF

\begin{bmatrix}<br /> 1 &amp; 0 &amp; \frac{15}{22} &amp; \frac{17}{11}\\ <br /> 0 &amp; 1 &amp; \frac{-3}{11}&amp; \frac{-9}{11}<br /> \end{bmatrix}So the basis is:
\begin{Bmatrix}<br /> \frac{-15}{22}\\ <br /> \frac{3}{11}\\ <br /> 1\\ <br /> 0<br /> \end{Bmatrix}, \begin{Bmatrix}<br /> \frac{-17}{11}\\ <br /> \frac{9}{11}\\ <br /> 0\\ <br /> 1<br /> \end{Bmatrix}

So now that I have U, W I am unsure on how to proceed with the addition and Union.

Should I just put both matrices ontop of one another and solve that ?
You don't need to check my bookwork just guidance on the general direction that I heading would be useful.

 

[sid9221]

Any one ?