Are These Vectors Linearly Independent?

[kiamax]

Homework Statement

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

Homework Equations

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?

 

[Mark44]

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