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sid9221
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http://dl.dropbox.com/u/33103477/Union.png
Omiting zeroes because they add nothing:
[tex] \begin{bmatrix}
3 & 1 & 7 & 4\\
5 & 6 & 7 & 3
\end{bmatrix}[/tex]
RREF
[tex] \begin{bmatrix}
1 & 0 & \frac{35}{13} & \frac{21}{13}\\
0 & 1 & \frac{-14}{13}& \frac{-11}{13}
\end{bmatrix} [/tex]
Hence the basis is:
[tex]
\begin{Bmatrix}
\frac{-35}{13}\\
\frac{14}{13}\\
1\\
0
\end{Bmatrix}, \begin{Bmatrix}
\frac{-21}{13}\\
\frac{11}{13}\\
0\\
1
\end{Bmatrix}[/tex]Similarly,
[tex] \begin{bmatrix}
6 & 4 & 3 & 6\\
4 & -1 & 3 & 7
\end{bmatrix}
[/tex]
RREF
[tex] \begin{bmatrix}
1 & 0 & \frac{15}{22} & \frac{17}{11}\\
0 & 1 & \frac{-3}{11}& \frac{-9}{11}
\end{bmatrix} [/tex]So the basis is:
[tex] \begin{Bmatrix}
\frac{-15}{22}\\
\frac{3}{11}\\
1\\
0
\end{Bmatrix}, \begin{Bmatrix}
\frac{-17}{11}\\
\frac{9}{11}\\
0\\
1
\end{Bmatrix} [/tex]
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.
Omiting zeroes because they add nothing:
[tex] \begin{bmatrix}
3 & 1 & 7 & 4\\
5 & 6 & 7 & 3
\end{bmatrix}[/tex]
RREF
[tex] \begin{bmatrix}
1 & 0 & \frac{35}{13} & \frac{21}{13}\\
0 & 1 & \frac{-14}{13}& \frac{-11}{13}
\end{bmatrix} [/tex]
Hence the basis is:
[tex]
\begin{Bmatrix}
\frac{-35}{13}\\
\frac{14}{13}\\
1\\
0
\end{Bmatrix}, \begin{Bmatrix}
\frac{-21}{13}\\
\frac{11}{13}\\
0\\
1
\end{Bmatrix}[/tex]Similarly,
[tex] \begin{bmatrix}
6 & 4 & 3 & 6\\
4 & -1 & 3 & 7
\end{bmatrix}
[/tex]
RREF
[tex] \begin{bmatrix}
1 & 0 & \frac{15}{22} & \frac{17}{11}\\
0 & 1 & \frac{-3}{11}& \frac{-9}{11}
\end{bmatrix} [/tex]So the basis is:
[tex] \begin{Bmatrix}
\frac{-15}{22}\\
\frac{3}{11}\\
1\\
0
\end{Bmatrix}, \begin{Bmatrix}
\frac{-17}{11}\\
\frac{9}{11}\\
0\\
1
\end{Bmatrix} [/tex]
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.
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