Let u be a linear combination of (ui, u2, u3) Select the best statement. A.(ui ,
ID: 3167405 • Letter: L
Question
Let u be a linear combination of (ui, u2, u3) Select the best statement. A.(ui , u2, u3} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. B. uu2, uz, u4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. C.,u2, us) is a linearly dependent set of vectors unless one of fui, u2, u is the zero vector. D. u, u2, ua is never a linearly dependent set of vectors. E. u, u2, u, u is never a linearly independent set of vectors. o F, {ui, u2, u3, u4) is always a linearty independent set of vectors. G. none of the aboveExplanation / Answer
Correct option:
E. {u1, u2, u3, u4} is never a linearly independent set of vectors.
EXPLANATION:
Given: u4 is a linear combination of {u1, u2, u3}. A set of 4 vectors can never be linearly independent set, if one vector is a linear combination of other 3 vectors.
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