Consider following five sets: 1. { <1, -1>, <1, 1> } { <0, 0> } II. { <1, -1> } II. IV. { <1, -1>, <1, 1>, <2 , 3> } V. { <1, -1>, <-2, 2> } Find all linearly dependent set(s). (a) I (b) I and IV (c) I and II (d) III, IV and V (e) II (f) III

Consider following five sets: 1. { <1, -1>, <1, 1> } { <0, 0> } II. { <1, -1> } II. IV. { <1, -1>, <1, 1>, <2 , 3> } V. { <1, -1>, <-2, 2> } Find all linearly dependent set(s). (a) I (b) I and IV (c) I and II (d) III, IV and V (e) II (f) III

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

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Consider following five sets:
1. { <1, -1>, <1, 1> }
{ <0, 0> }
II. { <1, -1> }
II.
IV. { <1, -1>, <1, 1>, <2 , 3> }
V. { <1, -1>,
<-2, 2> }
Find all linearly dependent set(s).
(a) I
(b) I and IV
(c) I and II
(d) III, IV and V
(e) II
(f) II

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