Consider the set of vectors that constitute the columns of the following matrix.1 1 210 121 XIs there a value of x that makes this set of vectors linearly dependent? If so, what is x? If not,explain why?

Answered: Consider the set of vectors that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Consider the set of vectors that constitute the columns of the following matrix.
1 1 2
1
0 1
2
1 X
Is there a value of x that makes this set of vectors linearly dependent? If so, what is x? If not,
explain why?

Expert Solution

Step 1: Introduction

Consider the set of vectors that constitute the columns of the following matrix

$open square brackets table row 1 cell space 1 end cell cell space 2 end cell row 1 cell space 0 end cell cell space 1 end cell row 2 cell space 1 end cell cell space x end cell end table close square brackets$

We have to find the value of x (if exist) that makes this set of vectors linearly dependent.

We know that

The set of vectors that constitute the columns of the matrix

A = $open square brackets table row a cell space d end cell cell space g end cell row b cell space e end cell cell space h end cell row c cell space f end cell cell space i end cell end table close square brackets$

is linearly dependent if $d e t open parentheses A close parentheses equals 0$ and linearly independent if $d e t open parentheses A close parentheses not equal to 0$