Kernel of Pokemon type chart (linear algebra)

[Yil]

I am too lazy to write a matrix calculator so I am still doing operations on a f*****g 18 by 18 matrix that I still don't know if it is invertible.
My senses tells me type:null and Arceus are each represented by a single basis in null space and left null space, but I don't know which is which even if that is true. And which type is left out? Should I switch type label when I switch rows?

 

[Deboog]

The kernal is just {0}

Just look at the first two lines of the thing. There is no way you can find a vector that will make both those 0.

 

[Yil]

The kernal is just {0}

Just look at the first two lines of the thing. There is no way you can find a vector that will make both those 0.

Not true. There are 16 independent vectors that are orthogonal to to the first two rows.