Answer
$\{(0,0,0,0)\}$.
Work Step by Step
The kernel of a linear map $T : A → B$, is the set of all elements $v$ in $A$ for which $T(v) = 0$, where $0$ is the zero vector in B.
Hence, here we need $(y.x,w,z)=(0,0,0,0)$. Thus $y=x=w=z=0$ and thus the kernel is $\{(0,0,0,0)\}$.
