Which of the following statements are true? I: 2v, +2v2 - 3v3 is an affine combination of the 3 vectors. I: III: The affine hull of two distinct points is a plane. If S= {x}, then aff S = {x}. IV: If a set of vectors in R" is linearly independent, then every vector in R" can be written as an affine combination of these vectors. O A. I and l| O B. I, III, and IV O C. I and III O D. Il and IV
Which of the following statements are true? I: 2v, +2v2 - 3v3 is an affine combination of the 3 vectors. I: III: The affine hull of two distinct points is a plane. If S= {x}, then aff S = {x}. IV: If a set of vectors in R" is linearly independent, then every vector in R" can be written as an affine combination of these vectors. O A. I and l| O B. I, III, and IV O C. I and III O D. Il and IV
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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
Transcribed Image Text:Which of the following statements are true?
I:
2v1 + 2v2 - 3v3 is an affine combination of the 3 vectors.
I:
The affine hull of two distinct points is a plane.
II:
If S= {x}, then aff S =
{x}.
%3D
IV:
If a set of vectors in R" is linearly independent, then every vector in R" can be written as an affine combination of these vectors.
A. I and II
B. 1, III, and IV
C. I and III
D. Il and IV
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