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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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?
Transcribed Image Text: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 (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

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