1. ## Span and Kernel

What would be the kernel of a 2x2 identity matrix. I put 0, I'm just making sure this is correct? Also, a 3x3 matrix 0 1 0, 0 0 1, 0 0 0. How would I do the kernel of this when x1 would be undefined?

2. Originally Posted by cwarga88
What would be the kernel of a 2x2 identity matrix. I put 0, I'm just making sure this is correct? Also, a 3x3 matrix 0 1 0, 0 0 1, 0 0 0. How would I do the kernel of this when x1 would be undefined?
Think about it like this... the identity matrix is really just the identity function and so if $v\ker I$ one has that $\bold{0}=Iv=v$ and so..

3. One thing it is useful to know- a square matrix is invertible if and only if its kernel contains only the 0 vector.