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}.%3DIV: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 IIB. 1, III, and IVC. I and IIID. Il and IV

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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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Concept explainers

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?
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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