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(52781)   (Show Source):
You can put this solution on YOUR website! .
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
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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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