
basis spanning R4
hi,
given two vectors:
$\displaystyle v_1=\left[\begin{array}{cc}1\\1\\1\\1\end{array}\right]$
and
$\displaystyle v_2=\left[\begin{array}{cc}1\\2\\3\\4\end{array}\right]$
i need to come up with two more vectors (eg U_1 and U_2) which when in a set with the first two create a basis for R^4. i tried using like a1,b1,c1,d1 for each u_1 and U_2 and getting it into REF but i had no joy. apparently according to my friend you should be able just to guess the vectors which satisfy this.
thanks,
(Headbang)

Adding for example $\displaystyle v_3=(0,0,1,0)^t,v_4=(0,0,0,1)^t$ you'll get a rank 4 matrix, that is the columns are linearly inedependent. Now use that $\displaystyle n$ linearly independent vectors in a vector space $\displaystyle V$ of dimension $\displaystyle n$ form a basis of $\displaystyle V$ .