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For three vectors to form a spanning set whether they should be linearly dependent or independent?

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Pls sum1 help
is a panning set "the most efficient" set?
if so, then all vectors of an efficient span should be INd

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I had a question asking to prove that a particular vector is not in the space spanned by other two vectors out of the three vectors given. Hw do I do that.
3 vectors with 3 components right?
there is a thrm in the book; got no idea which number for you;yas that if the rref matrix ov the vectors has a pivot in every row; then they are INd and you cannot create any particular vectorfrom a linear combonation of the other 2
in other words: 1 0 0 0 1 0 is the rref then you have INd vectors that cannot be created from the 0 0 1 other 2
i spose rref imight be a little further than needed to go; as long as there is a pivot in each row regardless you are good to go
What do you mean by pivot here?
pivot is a matrix term for .... well ... a leading number in a row that aint a zero
0034 3 is the pivot point
512 5 is your pivot point 002057 2 is your pivot point
Sorry I am nt very thorough with matrix cos I'v nt finishd learning yet. If I am to prove that I should show that the determinent is not equal to zero. Am I right?
determinate not=0 is prof enough in my book
10 01 det = 1 ; not zero; these are the vectors for the xy plane 12 48 det = 0 since they are the same vector; can be made from a linear combonation of the others
Thanx a lot. If u dnt mind shall I ask u a question.
yeah, at my age we dont really have a grade :) maybe the 35th or so

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