Linear independence?

  • #1
How do you know when a matrix (or equivocally a system of equations) is linearly independent? How do you know that it's linearly dependent?

For example, given this matrix,

[ 1 1 2 1]
[-2 1 4 0]
[ 0 3 2 2]

How do we know if this matrix is linearly independent or dependent?

Thanks! :)
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
How do you know when a matrix (or equivocally a system of equations) is linearly independent? How do you know that it's linearly dependent?

For example, given this matrix,

[ 1 1 2 1]
[-2 1 4 0]
[ 0 3 2 2]

How do we know if this matrix is linearly independent or dependent?

Thanks! :)

It isn't a matrix that is linearly dependent or independent. You can ask whether its rows or columns are. In this case the columns must be dependent because there are 4 of them and the columns have 3 components. To check whether the rows are dependent you would do row reduction. If a row becomes all 0 the rows are dependent.
 
  • #3
What do you mean by "3 components"?
 
  • #4
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,559
770
What do you mean by "3 components"?

Each column is a 3d column vector. It has, count 'em, three components.
 
  • #5
Each column is a 3d column vector. It has, count 'em, three components.

Ahhh. And by "components" you mean rows?
 

Related Threads on Linear independence?

  • Last Post
Replies
6
Views
780
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
851
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
2
Views
900
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
Top