1. ## basis spanning R4

hi,

given two vectors:

$v_1=\left[\begin{array}{cc}1\\1\\1\\1\end{array}\right]$

and

$v_2=\left[\begin{array}{cc}1\\2\\3\\4\end{array}\right]$

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,

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