Answer
$\{(a,a,s,-s):\text{$a,s$ are real}\}$.
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
$x_1-x_2=0\\x_1=x_2$, $x_2-x_1=0\\x_1=x_2$,$x_3+x_4=0\\x_3=-x_4.$
Thus the kernel is
$\{(a,a,s,-s):\text{$a,s$ are real}\}$.
