Question 9. The vectors vo, v1, ..., v, in Rm are said to be affinely independent if with scalars co, C1, ..., Cn, Eo CiV; = 0 and E, Ci = 0 implies c; = 0 for i = 0, 1, ..., n. For such an affinely...

The question is based on linear algebra. The correct option is D. Please provide a mathematical definition and explanation of 'affine independence'. Also, please provide a proof for Statement II to be linearly independent and statement I to be linearly dependent.

Thank you.

Extracted text: Question 9. The vectors vo, v1, ..., v, in Rm are said to be affinely independent if with scalars co, C1, ..., Cn, Eo CiV; = 0 and E, Ci = 0 implies c; = 0 for i = 0, 1, ..., n. For such an affinely independent set of vectors, which of the following is an implication: I. vo, V1, ..., Vn are linearly independent. II. (v1 – vo), (v2 – vo), ..., (Vn – vo) are linearly independent. III. n < m.="" (a)="" only="" i="" and="" ii="" are="" true="" (b)="" only="" i="" and="" iii="" are="" true="" (c)="" only="" ii="" is="" true="" (d)="" only="" ii="" and="" iii="" are="" true="">