SOLUTION: Determine if the vectors v1 = (1,2,3), v2 = (1,0,-1), v3 = (2,2,2), v4 = (2,4,6) span R^3 What I have done is create a matrix and Im not sure where to go next 1 2 3 1 0

Question 1054305: Determine if the vectors v1 = (1,2,3), v2 = (1,0,-1), v3 = (2,2,2), v4 = (2,4,6) span R^3
What I have done is create a matrix and Im not sure where to go next
1 2 3
1 0 -1
2 2 2
2 4 6
I assume I have to use Gaussian Elimination, but I am lost afterwards
Answer by ikleyn(52784) (Show Source): You can put this solution on YOUR website!
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Determine if the vectors v1 = (1,2,3), v2 = (1,0,-1), v3 = (2,2,2), v4 = (2,4,6) span R^3
What I have done is create a matrix and Im not sure where to go next

1  2  3       (1)
1  0  -1      (2)
2  2  2       (3)
2  4  6

I assume I have to use Gaussian Elimination, but I am lost afterwards
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check that just the vectors v1, v2 and v3 span R^3.

For it, it is enough to check that the determinant of the matrix (1), (2), (3) is non-zero.

Also, notice that vector v4 is collinear with vector v1.

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