Math Help - Linear Algebra....

1. Linear Algebra....

Missed class last week, and I'm not sure how to do this problem. I have three more like it, but if I can see the processes step-wise, I can do the others. Thanks.

Let S = (v1, v2, v3, v4, v5) where

v1=(1,1,0,-1)
v2=(0,1,2,1)
v3=(1,0,1,-1)
v4=(1,1,-6,-3)
v5=(-1,-5,1,0)

Find a basis for the subspace W=span S of R^4.
What is dim W?

and also...

Are the vectors bases for R³

{(1, 0, 0) , (0, 2, -1), (3, 4, 1) , (0, 1, 0)}

2. Originally Posted by amor_vincit_omnia
Missed class last week, and I'm not sure how to do this problem. I have three more like it, but if I can see the processes step-wise, I can do the others. Thanks.

Let S = (v1, v2, v3, v4, v5) where

v1=(1,1,0,-1)
v2=(0,1,2,1)
v3=(1,0,1,-1)
v4=(1,1,-6,-3)
v5=(-1,-5,1,0)

Find a basis for the subspace W=span S of R^4.
What is dim W?

and also...

Are the vectors bases for R³

{(1, 0, 0) , (0, 2, -1), (3, 4, 1) , (0, 1, 0)}
Make $\{v_1,v_2,...v_5 \}$ the row vectors in a matrix. Reduce the matrix to row eshelon form. The non zero row vectors will form a basis for the subspace they span of $\mathbb{R}^4$