# Homework Help: Constructing bases (worked out, please check !)

1. May 2, 2012

### sid9221

http://dl.dropbox.com/u/33103477/Union.png [Broken]

Omiting zeroes because they add nothing:

$$\begin{bmatrix} 3 & 1 & 7 & 4\\ 5 & 6 & 7 & 3 \end{bmatrix}$$

RREF

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

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

Similarly,

$$\begin{bmatrix} 6 & 4 & 3 & 6\\ 4 & -1 & 3 & 7 \end{bmatrix}$$

RREF

$$\begin{bmatrix} 1 & 0 & \frac{15}{22} & \frac{17}{11}\\ 0 & 1 & \frac{-3}{11}& \frac{-9}{11} \end{bmatrix}$$

So the basis is:
$$\begin{Bmatrix} \frac{-15}{22}\\ \frac{3}{11}\\ 1\\ 0 \end{Bmatrix}, \begin{Bmatrix} \frac{-17}{11}\\ \frac{9}{11}\\ 0\\ 1 \end{Bmatrix}$$

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.

Last edited by a moderator: May 6, 2017
2. May 3, 2012

Any one ?