Linear independent vectors

kiamax

Homework Statement

Determine whether the vector v1=(!,2,3),v2(3,2,1) and v3(1,1,1) are independent or dependent.

I'm so lost

The Attempt at a Solution

I'm so lost

Dustinsfl

Is that suppose to be ! or 1?

If it is suppose to be a 1, just put it in a matrix and do reduced row echelon form. If you don't get back the identity matrix, they aren't independent.

kiamax

I'm sorry that's suppose to be a 1

Dustinsfl

Ok, now just set up a 3 x 3 matrix and reduce the rows.

kiamax

When I set up the matrix and reduce the rows. This will show if its independent or independent?

Mentor

When I set up the matrix and reduce the rows. This will show if its independent or independent?
It will show whether the vectors are linearly independent or linearly dependent.

Dustinsfl

Yes, because if you don't obtain the identity matrix, one or two of the vectors are dependent.
[1,0,5]
[0,1,2]
[0,0,0]
Take this rref matrix as an example.
This is telling us the 3rd column can be written as 5v1+2v2.

kiamax

oh okay, thanks