Constructing bases (worked out, please check )

[sid9221]

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

Omiting zeroes because they add nothing:

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

RREF

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

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

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

RREF

$$\begin{bmatrix}<br /> 1 & 0 & \frac{15}{22} & \frac{17}{11}\\ <br /> 0 & 1 & \frac{-3}{11}& \frac{-9}{11}<br /> \end{bmatrix}$$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 ?