Math Is Fun Forum

Talvon

Member

Registered: 2006-11-15

Posts: 16

Checking for vectors being linearly independant

To check if a set of vectors are independent, do you just try and make a line equation out of them and it if doesn't work they are all independent of each other?

gnitsuk

Member

Registered: 2006-02-09

Posts: 121

Re: Checking for vectors being linearly independant

Let's say you have three vectors:

Then the set:

being linearly dependent implies and is implied by

So to give an exmaple of it's use - suppose we wish to determine if the set of vectors:

is linearly dependent or linearly independent:

We calculate:

This non-zero determinant shows that { (1,4,0),(1,4,3),(0,1,-1) } is linearly independent.

Last edited by gnitsuk (2006-11-22 21:46:26)

Talvon

Member

Registered: 2006-11-15

Posts: 16

Re: Checking for vectors being linearly independant

Awesome, thanks a lot