Solving Matrices with Standard Base Formula for Ker (T)

[transgalactic]

i am given a formula and asked to find the ker
of the matrices of the standart base

this is the link were i tried to solve it:

http://img297.imageshack.us/my.php?image=img7979ds0.jpg

when i try to find the ker (T)

i get all zeros

i don't know where i get it wrong

my theory says that after we simplify the matrix
A*(x,y,z)=(0,0,0)

so i built equation and all i get is all zeros
and that not the answer in the book
where did i got it wrong?

 

[transgalactic]

how to find ker (t) ??