Question:
Suppose {u, v, w} is a set of vectors in a vector space V.
Last updated: 7/27/2022
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Suppose {u, v, w} is a set of vectors in a vector space V. Which of the following statements is equivalent to "{u, v, w} is linearly independent"? I. None of the vectors u, v or w is a linear combination of the other vectors in {u, v, w}. II. None of the vectors u, v or w is a multiple of any other single vector in {u, v, w}. III. If a, b, c are scalars then au+by+cu=0 implies a = b = c=0. IV. If a b c = 0, then au + bv + cw = 0. mark (X) the correct answer: A I. and II. BI. and III. CI. and IV. D II. and III. E II. and IV. FIII. and IV.