# Vactor space

1. Mar 30, 2006

### UrbanXrisis

Find a linearly independent set of vectors that spans the same subspace of R^3 as that spanned by the vectors

$$\left(\begin{array}{c} -2 & -1 & -2 \end{array}\right) , \left(\begin{array}{c} -2 & 3 & -8 \end{array}\right) , \left(\begin{array}{c} 0 & -2 & 3 \end{array}\right)$$

I'm not sure how to find a linearly independent vector. For a linearly dependency, the determinant of the matrix cannot equal zero. But how would i find two other 3x1 vectors that does not have linear dependency?

2. Mar 30, 2006

### devious_

You could row reduce and look at the columns that correspond to the leading columns of your reduced matrix. Can you see why this would mean they're independent?

3. Mar 30, 2006