Consider following three sets: (i) set A has p vectors of the vector space V, and A= span{V}, (ii) set B has q linearly independent vectors of V, (iii) set C has r vectors of V, and C is the basis of V. Which of the following inequality is true? (Note: p, q, and r are distinct positive integers). (a) p

Consider following three sets: (i) set A has p vectors of the vector space V, and A= span{V}, (ii) set B has q linearly independent vectors of V, (iii) set C has r vectors of V, and C is the basis of V. Which of the following inequality is true? (Note: p, q, and r are distinct positive integers). (a) p

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

Consider following three sets:
(i) set A has p vectors of the vector space V, and A= span{V},
(ii) set B has q linearly independent vectors of V,
(iii) set C has r vectors of V, and C is the basis of V.
Which of the following inequality is true? (Note: p, q, and r are
distinct positive integers).
(a) p<r<q
(b) r<p<q
(c) q<p<r
(d) q<r<p
(e) r<q<p
Od
O e
a
Ob

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