Let V = {Z} be the set consisting of single element Z such that Z+ Z = Z and Vr E R, rZ = Z. Then which of the following is/are always correct? I. Vis a real vector space. II. V is a complex vector space. III. V is a subspace of the set of real numbers R. IV. V is a subspace of the set of complex numbers C. (a) Only I (b) Only II (c) Only I and III (d) Only II and IV (e) Only I, II and IV

Let V = {Z} be the set consisting of single element Z such that Z+ Z = Z and Vr E R, rZ = Z. Then which of the following is/are always correct? I. Vis a real vector space. II. V is a complex vector space. III. V is a subspace of the set of real numbers R. IV. V is a subspace of the set of complex numbers C. (a) Only I (b) Only II (c) Only I and III (d) Only II and IV (e) Only I, II 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

Let V = {Z} be the set consisting of single element Z such that Z+ Z = Z and Vr E R, rZ = Z.
Then which of the following is/are always correct?
I. Vis a real vector space.
II. V is a complex vector space.
III. V is a subspace of the set of real numbers R.
IV. V is a subspace of the set of complex numbers C.
(a) Only I
(b) Only II
(c) Only I and III
(d) Only II and IV
(e) Only I, II and IV

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