can you please provide explanations 4. For each of the following sets S of vectors in a vector space V, determine whether theelements of S are linearly independent or not and whether they span the whole of V. You mayuse the calculation techniques using matrices that you know from your previous linear algebramodules, even though we haven't got to them yet in this module!S = {(1, 2, 0), (2, 1, 3), (3, 0, -1)},S = {(1+i, 1-i), (i, 1), (2,1 + i)},V = R³,V = C².

The given set of vectors are:To determine: The elements of are linearly independent or not also…

Answered: 4. For each of the following sets S of…

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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Question

can you please provide explanations

4. For each of the following sets S of vectors in a vector space V, determine whether the
elements of S are linearly independent or not and whether they span the whole of V. You may
use the calculation techniques using matrices that you know from your previous linear algebra
modules, even though we haven't got to them yet in this module!
S = {(1, 2, 0), (2, 1, 3), (3, 0, -1)},
S = {(1+i, 1-i), (i, 1), (2,1 + i)},
V = R³,
V = C².

Expert Solution

Step 1: Introduction

The given set of vectors are:

$S equals open curly brackets open parentheses 1 comma 2 comma 0 close parentheses comma open parentheses 2 comma 1 comma 3 close parentheses comma open parentheses 3 comma 0 comma negative 1 close parentheses close curly brackets comma space V equals straight real numbers cubed S equals open curly brackets open parentheses 1 plus i comma 1 minus i close parentheses comma open parentheses i comma 1 close parentheses comma open parentheses 2 comma 1 plus i close parentheses close curly brackets comma space V equals straight complex numbers squared$

To determine: The elements of $S$ are linearly independent or not also they span the whole V or not.

Concept:

If the determinant of the se of vectors is non-zero then the elements in the set are linearly independent and vice versa.