Chapter 6 - Linear Transformations - 6.2 The Kernel and Range of a Linear Transformation - 6.2 Exercises - Page 312: 4

$\{(0,0,0)\}$.

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 $(z,y,x)=(0,0,0)$, so $y=x=z=0$, and thus the kernel is $\{(0,0,0)\}$.