**1. The problem statement, all variables and given/known data**

Let [tex]A = \left[\begin{array}{ccccc} 2&0&-2&1&-3 \\ 1&1&-3&0&-2\\1&0&-1&-1&3 \end{array}\right][/tex]

a) Find two linearly independent vectors u and v in R

^{5}such that span{u,v}={[tex]x \in R^5[/tex] : Ax=0}.

b) Find three linearly independent vectors u,v and w such that col(A) = span{u,v,w}.

**2. Relevant equations**

**3. The attempt at a solution**

a) I row reduced A:

[tex]\left[\begin{array}{ccccc} 1&0&-1&0&0 \\ 0&1&-2&0&-2\\0&0&0&1&-3 \end{array}\right][/tex]

I'm not sure how to answer this question. I think the first and second column are linearly independent and if we add them we get the third column. I need some help, I don't know what to do from here.

a) I row reduced A:

[tex]\left[\begin{array}{ccccc} 1&0&-1&0&0 \\ 0&1&-2&0&-2\\0&0&0&1&-3 \end{array}\right][/tex]

I'm not sure how to answer this question. I think the first and second column are linearly independent and if we add them we get the third column. I need some help, I don't know what to do from here.