# Linear algebra: Kernel/range

1. Mar 17, 2013

### Mdhiggenz

1. The problem statement, all variables and given/known data

Determine the kernel/range of each of the following linear operators on R3

L(X)=(x1,x1,x1)T

2. Relevant equations

3. The attempt at a solution

So first thing I did was create a 3x1 matrix filled with ones.

I equaled it to zero and found x1=0 to be a solution. However I'm not quite sure how they come up with the following answer.

(0,x2,x3). Also why would it be a 2 dimensional subspace? Would it be due to x1 being zero?

Thanks

Last edited by a moderator: Mar 17, 2013
2. Mar 17, 2013

### jbunniii

x1 = 0 if and only if the vector is of the form (0,x2,x3). The subspace spanned by vectors of this form has dimension 2 because for example {(0,1,0), (0,0, 1)} is a basis.

3. Mar 17, 2013

### Mdhiggenz

Perfect explanation. Thank you!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted