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set of vectors {v1, v2.......,vn} belongs to R^m where n<m. are vectors independent?
 one year ago
 one year ago
set of vectors {v1, v2.......,vn} belongs to R^m where n<m. are vectors independent?
 one year ago
 one year ago

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helder_edwinBest ResponseYou've already chosen the best response.1
not necesarily. for instance \[ \large \{(1,2,3),(0,0,0)\} \] is a linearly dependent set of two vectors in \(\mathbb{R}^3\) and \(2<3\).
 one year ago

bhutani_gBest ResponseYou've already chosen the best response.0
since you can prove that, for at least one case this is not true, therefore it can not be generalized.
 one year ago

AlfredTheGreatBest ResponseYou've already chosen the best response.0
To prove that (1,2,3) and (0,0,0) are dependent: Let us assume the contrary. If they are independent, then k1* (1,2,3) + k2 * (0,0,0) = (0,0,0) implies k1 = k2 = 0. But, in this case, only k1 has to be 0. k2 can be any number and the expression still holds. Hence the proof.
 one year ago
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