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

Question

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.

Kunduz · Accepted Answer

Click to see the answer