Question 378113: hello
How do i find the basis of a space spanned by a set of vectors v1 = (1,-2,0,0,3),v2=(2,-5,-3,-2,6),v3=(0,5,15,10,0),v4=(2,6,18,8,6). i tried it out assuming that if the space is spanned by these vectors then any arbitrary vector in R^5 can be found by a linear combination of these vector right? but i got no solution to an arbitrary vector of (3, 2, 4, 5, 6). if that is the case is it safe to say that no basis exists for a space spanned by v1, v2, v3, v4?
thanks for your help
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! If v1,v2,v3,v4 are linearly independent, the space spanned by them is 4 dimensional. It's a subspace of R^5.
If the vi's are linearly independent, they form a generating part of this lower dimensional sub-space (lower equals 3).
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