Which of the following statements are true for the set S= {v,, ..., V} in R"? 1: {v2 - v1, ..., Vk - v1} is linearly dependent if and only if S is affinely dependent. II: If S is affinely independent and a point p in R" has all positive barycentric coordinates determined by S, then p is not in aff S. A. Neither I or II В. I C. Both I and II O D. II

Which of the following statements are true for the set S= {v,, ..., V} in R"? 1: {v2 - v1, ..., Vk - v1} is linearly dependent if and only if S is affinely dependent. II: If S is affinely independent and a point p in R" has all positive barycentric coordinates determined by S, then p is not in aff S. A. Neither I or II В. I C. Both I and II O D. II

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Which of the following statements are true for the set S = {v,,..., v} in R"?
1: {v2 -V1,
Vk -v,} is linearly dependent if and only if S is affinely dependent.
II: If S is affinely independent and a point p in R" has all positive barycentric coordinates determined by S, then p is not in aff S.
A. Neither I or II
В. I
C. Both I and II
O D. II

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